question on a few things

science_man_88 · 2011-06-18, 18:25

most of you probably know of A002812 (a.k.a a(n) = 2a(n-1)^2 - 1, or a(n) = A003010(n)/2 ), and I want to ask a few questions about it:

1) has a(n) ever been expressed as a algebraic equation, especially using the fact that a(1) ( or a(2) depending on how you count it) is M3

and

2) if not, could this ever be used to find a pattern in the Mersenne numbers with prime exponents, that work out to be Mersenne primes. ( I mention this because they intersect and so we have a basis to form a relationship off which to base the relations between the two).

CRGreathouse · 2011-06-18, 20:56

Quote:

Originally Posted by science_man_88

has a(n) ever been expressed as a algebraic equation

No doubt. I imagine it's not too dissimilar to that of A003010.

science_man_88 · 2011-06-18, 21:07

Quote:

Originally Posted by CRGreathouse

No doubt. I imagine it's not too dissimilar to that of A003010.

it's based on it.

science_man_88 · 2011-06-18, 21:47

Quote:

Originally Posted by science_man_88

it's based on it.

a(n) = 2a(n-1)^2 - 1 comes about by $x^2-2=4y^2 -2$ when x is even, and so $\frac{4y^2-2}{2} = 2y^2-1$ but I was more leaning towards in relation to p=3 as a(1)=2^3-1 =7.

science_man_88 · 2011-06-18, 22:21

Quote:

Originally Posted by science_man_88

a(n) = 2a(n-1)^2 - 1 comes about by $x^2-2=4y^2 -2$ when x is even, and so $\frac{4y^2-2}{2} = 2y^2-1$ but I was more leaning towards in relation to p=3 as a(1)=2^3-1 =7.

A000225 and A002812 have 7 in common from that common value on using algebra can we figure out what elements will divide each other ?

$2*(2^p-1)^2-1 = 2(2^{2p}-2^{p+1}+1)-1 = 2^{2p+1}-2^{p+2}+2-1 = 2^{2p+1}-2^{p+2}+1$ I went one step further into A002818 than this but I'll currently save you on that part.

so I'm trying to relate 2^{p+k}-1 to this sequence is their a general formula outside of just doing $(a+b+c)^2 = a^2+ab+ac+ba+b^2+bc+ca+cb+c^2 =a^2+b^2+c^2+2(ab)+2(ac)+2(bc)$ to relate it back to the known p=3 they rely on ?

science_man_88 · 2011-06-18, 23:18

anybody confused about what I mean ?

R.D. Silverman · 2011-06-19, 00:31

Quote:

Originally Posted by science_man_88

anybody confused about what I mean ?

You certainly are.

science_man_88 · 2011-06-19, 00:32

Quote:

Originally Posted by science_man_88

anybody confused about what I mean ?

Quote:

0, 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023,

Quote:

2, 7, 97, 18817, 708158977, 1002978273411373057,

the bolder term is where they meet any term in either after this should be able to be related back to that term and hence to terms of the other (especially since these sequences can be used with each other). 2^k(2^p-1)+(2^k-1) = M_p+k so is there a simple relation for the other that we can then make a relation between the relations from ?

science_man_88 · 2011-06-19, 00:34

Quote:

Originally Posted by R.D. Silverman

You certainly are.

Doh! , I knew that was coming. I'm more confusing , mostly to others but, sometimes I confuse myself.

science_man_88 · 2011-06-19, 12:33

however I know I'm not confused just having trouble getting my point across, no surprises there.

science_man_88 · 2011-06-19, 16:31

Quote:

Originally Posted by R.D. Silverman

You certainly are.

What's your reasoning for that comment? I'd love to know!

2011-06-18, 18:25	#1
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶×131 Posts	question on a few things most of you probably know of A002812 (a.k.a a(n) = 2a(n-1)^2 - 1, or a(n) = A003010(n)/2 ), and I want to ask a few questions about it: 1) has a(n) ever been expressed as a algebraic equation, especially using the fact that a(1) ( or a(2) depending on how you count it) is M3 and 2) if not, could this ever be used to find a pattern in the Mersenne numbers with prime exponents, that work out to be Mersenne primes. ( I mention this because they intersect and so we have a basis to form a relationship off which to base the relations between the two). Last fiddled with by science_man_88 on 2011-06-18 at 18:29 Reason: added in and then bolded the bad word everyone hates

2011-06-18, 23:18	#6
science_man_88 "Forget I exist" Jul 2009 Dumbassville 20C0₁₆ Posts	anybody confused about what I mean ? Last fiddled with by science_man_88 on 2011-06-18 at 23:39

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2011-06-19, 12:33	#10
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶·131 Posts	however I know I'm not confused just having trouble getting my point across, no surprises there.