cp's OEIS Frontend

A226251 Period 10: repeat [1, 1, 2, 3, 5, 8, 1, 3, 4, 7].

%I A226251 #43 May 29 2025 10:48:09
%S A226251 1,1,2,3,5,8,1,3,4,7,1,1,2,3,5,8,1,3,4,7,1,1,2,3,5,8,1,3,4,7,1,1,2,3,
%T A226251 5,8,1,3,4,7,1,1,2,3,5,8,1,3,4,7,1,1,2,3,5,8,1,3,4,7,1,1,2,3,5,8,1,3,
%U A226251 4,7,1,1,2,3,5,8,1,3,4,7,1,1,2,3,5,8,1,3,4,7
%N A226251 Period 10: repeat [1, 1, 2, 3, 5, 8, 1, 3, 4, 7].
%C A226251 Previous name was: Concatenated cyclical sequence starting from Fibonacci sequence.
%C A226251 Start with the Fibonacci sequence 0,1,1,2,3,5,8; at this point rewrite the next term 13 as 1,3 and continue adding: 1,3,4,7. At this point rewrite the sum 11 as 1,1 and the sequence will recur if values greater than or equal to 10 are rewritten as two single-digit values as 0,1,1,2,3,5,8,1,3,4,7,1,1,2,3,5,8,1,3,4,7,1,1,...
%H A226251 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1).
%e A226251 1) (9,9) 9,9,1,8,9,1,7,8,1,5,6,1,1,2,3,5,8,1,3,4,7,1, 1, 2, 3, 5, 8, 1, 3, 4, 7, ...
%e A226251 2) (3,7) 3,7,9,1,6,7,1,3,4,7,1,1,2,3,5,8,1,3,4,7,1, 1, 2, 3, 5, 8, 1, 3, 4, 7, ...
%e A226251 3) (0,4) 0,4,4,8,1,2,3,5,8,1,3,4,7,1,1,2,3,5,8,1,3,4,7,1, 1, 2, 3, 5, 8, 1, 3, 4, 7, ...
%e A226251 However if the sequence starts with one of the following, (0,7),(1,4),(2,6),(3,1),(4,2),(4,5),(5,9),(6,8),(7,0),(7,7),(8,6),(9,5) the sequence converges to 1,4,5,9 which is listed as a subsequence of A000285. For all but the trivial exception (0,0) the rest of the two-digit combinations when added together will generate the sequence.
%t A226251 nxt[{a_,b_}]:=If[b>9,IntegerDigits[b],{b,a+b}]; NestList[nxt,{1,1},120][[All,1]] (* _Harvey P. Dale_, Jan 07 2020 *)
%t A226251 PadRight[{},120,{1,1,2,3,5,8,1,3,4,7}] (* _Harvey P. Dale_, Jan 07 2020 *)
%K A226251 nonn,base,easy,less
%O A226251 1,3
%A A226251 _Lynn R. Purser_, Jun 03 2013
%E A226251 More terms from _Harvey P. Dale_, Jan 07 2020
%E A226251 New name from _Joerg Arndt_, May 29 2025