A108564 a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 2, a(4) = 4, for n>3: a(n+1) = SORT[a(n) + a(n-1) + a(n-2) + a(n-3)], where SORT places digits in ascending order and deletes 0's.

0, 1, 1, 2, 4, 8, 15, 29, 56, 18, 118, 122, 134, 239, 136, 136, 456, 679, 147, 1148, 234, 228, 1577, 1378, 1347, 345, 4467, 3577, 3679, 1268, 11299, 12389, 23568, 24458, 11477, 12789, 22279, 137, 24668, 35789, 23788, 23488, 13377, 24469, 12258, 23579

Offset

0,4

Comments

Sorted tetranacci numbers, a.k.a. sorted Fibonacci 4-step sequence.

As found by T. D. Noe: Max=4556699. Cycle period=41652. Cycle starts with the 23944th term.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Richard I. Hess, Problem 920: sorted Fibonacci sequence, Pi Mu Epsilon Journal, Vol. 10 (Fall 1998) No. 9, pp. 754-755.

Example

a(8) = SORT[a(4) + a(5) + a(6) + a(7)] = SORT[108] = 18.
a(10) = SORT[a(6) + a(7) + a(8) + a(9)] = SORT[221] = 122.

Mathematica

nxt[{a_, b_, c_, d_, e_}]:={b, c, d, e, FromDigits[Sort[DeleteCases[ IntegerDigits[ b+c+d+e], _?0]]]}; NestList[nxt, {0, 1, 1, 2, 4}, 50][[All, 1]] (* Harvey P. Dale, Jan 17 2022 *)

Crossrefs

Cf. A000078, A069638, A107281, A108565-A108573.

Sequence in context: A278554 A335473 A224959 * A066369 A239555 A275544

Adjacent sequences: A108561 A108562 A108563 * A108565 A108566 A108567

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Jun 10 2005

Status

approved