OFFSET
1,3
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,...
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1).
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn,base,easy,less
AUTHOR
Lynn R. Purser, Jun 03 2013
EXTENSIONS
More terms from Harvey P. Dale, Jan 07 2020
New name from Joerg Arndt, May 29 2025
STATUS
approved