[seqfan] More and more commas

Éric Angelini bk263401 at skynet.be
Tue May 12 19:38:52 CEST 2020

[Brussels, May 12 2020, 19:40]
Hello SeqFans,
We want to read the sum a(n) + a(n+1) around the comma coming immediately after a(n+1).
This is easy to build from a(1) = 1 on and might produce a nice sequence.

S = 1,11,23,46,91,374,6506,8801,53076,18777,18533,...

a(1)=1 + a(2)=11 is 12 and 12 is visible around the comma following 11:

S = 1,11,23,

a(2)=11 + a(3)=23 is 34 and 34 is visible around the comma following 23:

S = 1,11,23,46,

a(3)=23 + a(4)=46 is 69 and 69 is visible around the comma following 46:

S = 1,11,23,46,91,

a(4)=46 + a(5)=91 is 137 and 137 is visible around the comma following 91:

S = 1,11,23,46,91,374,

The rule here is that the rightmost digit of a(n+1) is the first digit of the sum a(n) + a(n+1), the other digits of the said sum being put after the comma in order to start a(n+2).
As no digit 0 (zero) can start a term, one will have to backtrack sometimes – and pick another term for a(n+1), compatible with the above rule.
This is always possible. We will try though to extend the sequence S as far as possible with the smallest available integer not yet present in S.

The nice part of this idea is that S is not monotonically increasing (look at the last three terms of the sequence that opens the page): who knows how it will behave in the future?

More can be said about S, but enough for today!
(some color and highlights here, on my personal blog: https://bit.ly/3brFiSz)

More information about the SeqFan mailing list