A108565 a(0) = 0, a(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) + a(n-4)], where SORT places digits in ascending order and deletes 0's.

0, 1, 1, 2, 4, 8, 16, 13, 34, 57, 128, 248, 48, 155, 366, 459, 1267, 2259, 456, 478, 1499, 5599, 1129, 1169, 4789, 11458, 12444, 3899, 33579, 16669, 4789, 1378, 1346, 15677, 35899, 5899, 1699, 256, 3459, 12247, 2356, 127, 14458, 23467, 25556, 45669, 12779

Offset

0,4

Comments

Sorted Pentanacci Numbers, a.k.a. Sorted Fibonacci 5-step Sequence.

Corrected and extended by T. D. Noe, who also found that Max = 334566999 occurs at a(67701). However, this is the only time that the maximum occurs. The cycle period has length 251784 and begins at a(1183787). Primes include: a(3) = 2, a(7) = 13, a(20) = 1499, a(22) = 1129, a(24) = 4789, a(30) = 4789, a(34) = 35899, a(36) = 1699, a(41) = 127, a(52) = 124577, a(62) = 33889, a(66) = 1579, a(67) = 25667, a(71) = 2789, a(80) = 4567, a(82) = 57899, a(87) = 23399, a(89) = 245899, a(90) = 349, a(93) = 346669. Semiprimes include: a(4) = 4 = 2^2, a(8) = 34 = 2 * 17, a(9) = 57 = 3 * 19, a(13) = 155 = 5 * 31, a(16) = 1267 = 7 * 181, a(19) = 478 = 2 * 239, a(21) = 5599 = 11 * 509, a(23) = 1169 = 7 * 167, a(27) = 3899 = 7 * 557, a(29) = 16669 = 79 * 211, a(32) = 1346 = 2 * 673, a(33) = 15677 = 61 * 257, a(35) = 5899 = 17 * 347, a(38) = 3459 = 3 * 1153, a(39) = 12247 = 37 * 331, a(42) = 14458 = 2 * 7229, a(43) = 23467 = 31 * 757, a(46) = 12779 = 13 * 983, a(48) = 12779 = 13 * 983, a(51) = 234557 = 163 * 1439, a(53) = 47899 = 19 * 2521, a(54) = 12459 = 3 * 4153, a(58) = 158 = 2 * 79, a(60) = 22299 = 3 * 7433, a(64) = 4579 = 19 * 241, a(65) = 689 = 13 * 53, a(70) = 24599 = 17 * 1447, a(74) = 26678 = 2 * 13339, a(75) = 1579, a(77) = 16789 = 103 * 163, a(78) = 2489 = 19 * 131, a(84) = 111379 = 127 * 877, a(85) = 122333 = 71 * 1723, a(86) = 34899 = 3 * 11633, a(99) = 1344479 = 17 * 79087, a(100) = 1245889 = 337 * 3697.

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(3) + a(4) + a(5) + a(6) + a(7)] = SORT[61] = 16.

Mathematica

nxt[{a_, b_, c_, d_, e_}]:={b, c, d, e, FromDigits[Select[Sort[ IntegerDigits[ a+b+c+d+e]], #!=0&]]}; NestList[nxt, {0, 1, 1, 2, 4}, 50][[All, 1]]

Crossrefs

Cf. A001591, A069638, A107281, A108564, A108566-A108573.

Sequence in context: A036120 A334629 A358708 * A066005 A066600 A210025

Adjacent sequences: A108562 A108563 A108564 * A108566 A108567 A108568

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Jun 10 2005

Status

approved