cp's OEIS Frontend

A334829 The sum a(n) + a(n+1) is visible around the comma that follows a(n+1). See the Comments and Example sections for details.

%I A334829 #14 Jan 08 2025 11:21:34
%S A334829 1,11,23,46,91,374,6506,8801,53076,18777,18533,73109,16428,95371,
%T A334829 117992,133632,516246,4987805,50405105,539291005,896961101,4362521065,
%U A334829 2594821666,9573427311,21682489773,12559170843,42416606165,49757770089,21743762547,15015326363,67590889108,26062154719,36530438276,25925929956
%N A334829 The sum a(n) + a(n+1) is visible around the comma that follows a(n+1). See the Comments and Example sections for details.
%C A334829 The rule used 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).
%C A334829 As no digit 0 (zero) can start a term, one will have to backtrack sometimes in order to extend the sequence - and pick another term for a(n+1), compatible with the above rule. This is always possible.
%C A334829 Note that the sequence is not monotonically increasing as shown by a(10) and a(11) for instance; still, the 1000th term is 406-digit long.
%C A334829 The sequence is always extended with the smallest available integer not yet present that does not lead to a contradiction.
%H A334829 Jean-Marc Falcoz, <a href="/A334829/b334829.txt">Table of n, a(n) for n = 1..1002</a>
%H A334829 E. Angelini <a href="https://web.archive.org/web/20201230071316/http://list.seqfan.eu/pipermail/seqfan/2020-May/020717.html">More and more commas</a> on the SeqFan mailing list, May 12 2020.
%e A334829 a(1) + a(2) is 1 + 11 = 12 and 12 can be seen here: 1(1,2)3,
%e A334829 a(2) + a(3) is 11 + 23 = 34 and 34 can be seen here: 2(3,4)6,
%e A334829 a(3) + a(4) is 23 + 46 = 69 and 69 can be seen here: 4(6,9)1,
%e A334829 a(4) + a(5) is 46 + 91 = 137 and 137 can be seen here: 9(1,37)4,
%e A334829 a(5) + a(6) is 91 + 374 = 465 and 465 can be seen here: 37(4,65)06, etc.
%Y A334829 Cf. A121805, A230450, A197756.
%K A334829 base,nonn
%O A334829 1,2
%A A334829 _Eric Angelini_ and _Jean-Marc Falcoz_, May 13 2020