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2020-10-15, 12:47   #23
Dr Sardonicus

Feb 2017
Nowhere

357910 Posts

Quote:
 Originally Posted by Uncwilly 3, 4, 9, 8, 9, 9, 8, 9, 9, 8...
I'll state an obvious answer, the digits of the decimal expansion of 34/100 + 989/99900 = 6991/19980.

2020-10-15, 13:41   #24
Uncwilly
6809 > 6502

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Aug 2003
101×103 Posts

2×4,373 Posts

Quote:
 Originally Posted by Dr Sardonicus I'll state an obvious answer, the digits of the decimal expansion of 34/100 + 989/99900 = 6991/19980.
three (5) + four (4) = nine (4)
four (4) + nine (4) = eight (5)
nine (4) + eight (5) = nine (4)
nine (4) + nine (4) = eight (5)
and around we go
The sum of the letters leads to the next number in sequence.
one (3) + two (3) = six (3) loops right away

2020-10-15, 15:28   #25
Dr Sardonicus

Feb 2017
Nowhere

3×1,193 Posts

Quote:
 Originally Posted by Uncwilly three (5) + four (4) = nine (4) four (4) + nine (4) = eight (5) nine (4) + eight (5) = nine (4) nine (4) + nine (4) = eight (5) and around we go The sum of the letters leads to the next number in sequence. one (3) + two (3) = six (3) loops right away
What about the sequence that begins 1, 3, ...?

2020-10-15, 19:52   #26
Uncwilly
6809 > 6502

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Aug 2003
101×103 Posts

222A16 Posts

Quote:
 Originally Posted by Dr Sardonicus What about the sequence that begins 1, 3, ...?
What about 5, 6 ? There are others 1, 1 or 2, 2 or 3, 3

2020-10-16, 00:32   #27
Dr Sardonicus

Feb 2017
Nowhere

3×1,193 Posts

Quote:
 Originally Posted by Uncwilly What about 5, 6 ? There are others 1, 1 or 2, 2 or 3, 3

 2020-10-16, 05:10 #28 R2357   "Ruben" Oct 2020 Nederland 37 Posts 1, 3 I would guess the triangular numbers, at least, it's a possibility.
2020-10-16, 11:52   #29
Dr Sardonicus

Feb 2017
Nowhere

3·1,193 Posts

Quote:
 Originally Posted by R2357 I would guess the triangular numbers, at least, it's a possibility.
No, Uncwilly gave the rule: Add the number of letters in the (English) names for two consecutive digits to get the next digit.

This would appear to be problematic when you start with 1, 3. Hence my question.

Of the 81 pairs of initial nonzero decimal digits, 36 of them cause the same problem.

2020-10-16, 12:04   #30
Viliam Furik

Jul 2018
Martin, Slovakia

223 Posts

Quote:
 Originally Posted by Dr Sardonicus No, Uncwilly gave the rule: Add the number of letters in the (English) names for two consecutive digits to get the next digit. This would appear to be problematic when you start with 1, 3. Hence my question. Of the 81 pairs of initial nonzero decimal digits, 36 of them cause the same problem.
1 (one) + 3 (three) -> 8 (eight)
3 (three) + 8 (eight) -> 10 (ten)
8 (eight) + 10 (ten) -> 8 (eight)...

The sequence would continue into infinity, alternating between 8 and 10.

I can see is that 3,8,? is a bit problematic, because of the number ten not being a single digit. 1,3,? is not problematic, you can do it, but AFTER that comes trouble.

If you extend the sequence rule to a number of letters in the name of the number, it becomes possible to do every starting value (I think).

2020-10-16, 12:22   #31
Dr Sardonicus

Feb 2017
Nowhere

3·1,193 Posts

Quote:
 Originally Posted by Viliam Furik 1 (one) + 3 (three) -> 8 (eight) 3 (three) + 8 (eight) -> 10 (ten) 8 (eight) + 10 (ten) -> 8 (eight)... The sequence would continue into infinity, alternating between 8 and 10. I can see is that 3,8,? is a bit problematic, because of the number ten not being a single digit. 1,3,? is not problematic, you can do it, but AFTER that comes trouble.
Yes, ten is not a decimal digit.

Another possibility is to interpret a sum of 10 as 1,0.

This is precisely why I asked Uncwilly. It was his rule, so it's his call on what to do when the rule gives a not-a-decimal-digit next term.

2020-10-16, 13:37   #32
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

2·4,373 Posts

Quote:
 Originally Posted by Dr Sardonicus Yes, ten is not a decimal digit.
That is where you make an issue. I said number. You assumed digit.

2020-10-16, 19:24   #33
Dr Sardonicus

Feb 2017
Nowhere

3·1,193 Posts

Quote:
 Originally Posted by Uncwilly I said number. You assumed digit.
So you did, and so I did.

Hmm. The question of what starting values give bounded sequences is more interesting than I thought!

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