A108567 a(0) = 0, a(1) = a(2) = 1, a(3) = 2, a(4) = 4, a(5) = 8, a(6) = 16, for n>5: a(n+1) = SORT[ a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6)], where SORT places digits in ascending order and deletes 0's.

0, 1, 1, 2, 4, 8, 16, 23, 55, 19, 127, 225, 347, 128, 249, 115, 112, 133, 139, 1223, 299, 227, 2248, 1348, 1567, 157, 679, 2556, 2788, 11334, 2249, 1233, 2699, 23358, 12467, 12568, 5689, 2366, 368, 15559, 23577, 24579, 4678, 16678, 5788, 12279, 11338

Offset

0,4

Comments

T. D. Noe found that the maximum is attained at a(4992871827) = 234444568999. The periodic part of this sequence begins at a(3544675600) and has length 5158842780.

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(7) = SORT[a(0) + a(1) + a(2) + a(3) + a(4) + a(5) + a(6)] = SORT[0 + 1 + 1 + 2 + 4 + 8 + 16] = SORT[32] = 23.
a(8) = SORT[a(1) + a(2) + a(3) + a(4) + a(5) + a(6) + a(7)] = SORT[1 + 1 + 2 + 4 + 8 + 16 + 23] = SORT[55] = 55.
a(9) = SORT[a(2) + a(3) + a(4) + a(5) + a(6) + a(7) + a(8)] = SORT[1 + 2 + 4 + 8 + 16 + 23 + 55] = SORT[109] = 19.

Mathematica

nxt[{a_, b_, c_, d_, e_, f_, g_}]:={b, c, d, e, f, g, FromDigits[Sort[ IntegerDigits[ a+b+c+d+e+f+g]/.(0->Nothing)]]}; NestList[nxt, {0, 1, 1, 2, 4, 8, 16}, 50][[All, 1]] (* Harvey P. Dale, May 09 2020 *)

Crossrefs

Cf. A066178, A069638, A107281, A108564-A108566, A108568-A108573.

Sequence in context: A057615 A018416 A028909 * A354754 A261890 A072874

Adjacent sequences: A108564 A108565 A108566 * A108568 A108569 A108570

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Jun 11 2005

Status

approved