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 2022-08-21, 09:14 #1 Paimon2005     "51*462^463-1" Jul 2022 Fujian Prov, China 23 Posts Interesting Facts of OEIS A003010 OEIS A003010 is a interesting sequence, You can use this formula to get it $a_n=a_{n-1}^2-2,a_0=4$ Today we will tell you some interesting Facts of OEIS A003010 1.$a_n$ mod 10 always equals to 4 2.If you convert a lot numbers of A003010 into binary, you will get: Code: 1110 11000010 1001001100000010 1010100011010110100110000000010 1101111010110100101101101100111110000001111010011000000000010 11000001101111011110110010100001011110111010101101011111011000110011001000100001000000011110101001111101001100000000000010 1001001010011111111010111011001010111101101000110010001010111111001010110011100011001001001101000011001001000111011011101111011111100110101000000110110011100011001101011101111000010101010101011001100111111001110100110111110100110000000000000010 1010011111110101100110010111110100000010101011101001001001111001111101111100110000010100111111101011110100001111100100111010111100100100100000010100011111000010011001011010101110010110111000000100110001110111000100111011100011000001011101100000010111010011001100100010001101100000101001001111010110011111110100011001000001010110011000010000010111010100001100111111000010100001110101001110111011011011001101100010010001000001111010001100000110101100101110111011111010011000000000000000010 1101110001100100101100111100000001111101100110110001111011111111100100001011000100101101010011111010010001000001001001111000001111010101001000100111000111001000010110100100010000110111000101111011100000101111011010000110111100111011011000001011001101101110011000101111011110011111001100101111001001100100010111110010000001011100011001001001111001000111001000101000100101100001010101111111100000111010100100011011101001110101011010101110101110101111101110000001111110001011011011101010010011110111011100101001110001111101100111000000100011101101111110111001001001111000000100111100100010010000000110001101101010010000001111001001010011001010110100010001100111101110011011010010000000111010011101101000100101111011010101110100001001100110100100101101111111100001101110110100000101010011100010101110011000101000010000110100101101000011010011100111110001111011000100101000000001000101001001111110110110101010000101110000110000000110110000000011101111101001100000000000000000010 To be convenient read, we add zeros at the start of lines to make them have the same length Code: 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001110 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011000010 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000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001101111010110100101101101100111110000001111010011000000000010 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011000001101111011110110010100001011110111010101101011111011000110011001000100001000000011110101001111101001100000000000010 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001001001010011111111010111011001010111101101000110010001010111111001010110011100011001001001101000011001001000111011011101111011111100110101000000110110011100011001101011101111000010101010101011001100111111001110100110111110100110000000000000010 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001010011111110101100110010111110100000010101011101001001001111001111101111100110000010100111111101011110100001111100100111010111100100100100000010100011111000010011001011010101110010110111000000100110001110111000100111011100011000001011101100000010111010011001100100010001101100000101001001111010110011111110100011001000001010110011000010000010111010100001100111111000010100001110101001110111011011011001101100010010001000001111010001100000110101100101110111011111010011000000000000000010 110111000110010010110011110000000111110110011011000111101111111110010000101100010010110101001111101001000100000100100111100000111101010100100010011100011100100001011010010001000011011100010111101110000010111101101000011011110011101101100000101100110110111001100010111101111001111100110010111100100110010001011111001000000101110001100100100111100100011100100010100010010110000101010111111110000011101010010001101110100111010101101010111010111010111110111000000111111000101101101110101001011110111011100101001110001111101100111000000100011101101111110111001001001111000000100111100100010010000000110001101101010010000001111001001010011001010110100010001100111101110011011010010000000111010011101101000100101111011010101110100001001100110100100101101111111100001101110110100000101010011100010101110011000101000010000110100101101000011010011100111110001111011000100101000000001000101001001111110110110101010000101110000110000000110110000000011101111101001100000000000000000010 You will found that except first line, the other lines are all end up in "10". Except first and second lines, at the left of the last "10", you will found a chain which is made of some zeros, and the length of the chain of 3rd line is 4, and that of 4th is 6, 5th is 8, 6th is 10, every line adds 2 zeros. Well, at the left of every zeros chain, you can see "0011" 3.If you deleted "0011...00...0010" at the end of every lines since 3rd lines in No.2 ,you can see Code: 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001001 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00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011000001101111011110110010100001011110111010101101011111011000110011001000100001000000011110101001111101 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010010010100111111110101110110010101111011010001100100010101111110010101100111000110010010011010000110010010001110110111011110111111001101010000001101100111000110011010111011110000101010101010110011001111110011101001101111101 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101001111111010110011001011111010000001010101110100100100111100111110111110011000001010011111110101111010000111110010011101011110010010010000001010001111100001001100101101010111001011011100000010011000111011100010011101110001100000101110110000001011101001100110010001000110110000010100100111101011001111111010001100100000101011001100001000001011101010000110011111100001010000111010100111011101101101100110110001001000100000111101000110000011010110010111011101111101 00000000000000110111000110010010110011110000000111110110011011000111101111111110010000101100010010110101001111101001000100000100100111100000111101010100100010011100011100100001011010010001000011011100010111101110000010111101101000011011110011101101100000101100110110111001100010111101111001111100110010111100100110010001011111001000000101110001100100100111100100011100100010100010010110000101010111111110000011101010010001101110100111010101101010111010111010111110111000000111111000101101101110101001011110111011100101001110001111101100111000000100011101101111110111001001001111000000100111100100010010000000110001101101010010000001111001001010011001010110100010001100111101110011011010010000000111010011101101000100101111011010101110100001001100110100100101101111111100001101110110100000101010011100010101110011000101000010000110100101101000011010011100111110001111011000100101000000001000101001001111110110110101010000101110000110000000110110000000011101111101 Since the 2nd line(4th line in No.2), the last 2 digits of every line are same, the 3rd line(5th line in No.2), the last 4 digits of every line are same, the 4th line(6th line in No.2), the last 6 digits of every line are same.(Every line adds 2 digits) If you have a deep research on A003010, you will found more interesting facts. Last fiddled with by S485122 on 2022-08-21 at 12:12 Reason: Do you intend to duplicate all threads and posts ? This not the way the forum works.
 2022-08-23, 15:00 #2 Paimon2005     "51*462^463-1" Jul 2022 Fujian Prov, China 816 Posts For the reason the Chinese Version of the post, see #3 Last fiddled with by Paimon2005 on 2022-08-23 at 15:04
 2022-08-23, 15:01 #3 Paimon2005     "51*462^463-1" Jul 2022 Fujian Prov, China 23 Posts In that time I put 2 posts, though their meaning was similar, one(this) was written in English, another was written in Chinese. But the post which was written in Chinese was deleted by the forum because the forum thought I intended to duplicate. Last fiddled with by Paimon2005 on 2022-08-23 at 15:06

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