A226251 Period 10: repeat [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, 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, 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, 4, 7

Offset: 1

Author

Lynn R. Purser, Jun 03 2013

Keywords

• nonn
• base
• easy
• less

Comments

Previous name was: Concatenated cyclical sequence starting from Fibonacci sequence.

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,...

Examples

			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, ...
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, ...
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, ...
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.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1).

Programs

Mathematica

nxt[{a_,b_}]:=If[b>9,IntegerDigits[b],{b,a+b}]; NestList[nxt,{1,1},120][[All,1]] (* Harvey P. Dale, Jan 07 2020 *)
PadRight[{},120,{1,1,2,3,5,8,1,3,4,7}] (* Harvey P. Dale, Jan 07 2020 *)

Extensions

More terms from Harvey P. Dale, Jan 07 2020

New name from Joerg Arndt, May 29 2025