A108566 a(0) = 0, a(1) = a(2) = 1, a(3) = 2, a(4) = 4, a(5) = 8, for n>4: a(n+1) = SORT[ a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5)], where SORT places digits in ascending order and deletes 0's.

0, 1, 1, 2, 4, 8, 16, 23, 45, 89, 158, 339, 67, 127, 258, 138, 178, 117, 588, 146, 1245, 1224, 3489, 689, 1378, 1178, 239, 1789, 2678, 1579, 1488, 1589, 2369, 11249, 2259, 2335, 12289, 239, 347, 12788, 2357, 3355, 13357, 23344, 45558, 1579, 5589

Offset: 0

Author

Jonathan Vos Post, Jun 10 2005

Keywords

• base
• easy
• nonn

Comments

Extended by T. D. Noe, who also found that verified that the maximum is attained at a(48968063)=12336789999. The periodic part of the sequence begins with a(4847516) and has length 156501072. So the maximum is in the periodic part. Primes include: a(3) = 2, a(7) = 23, a(9) = 89, a(12) = 67, a(13) = 127, a(27) = 1789, a(29) = 1579, a(36) = 12289, a(37) = a(26) = 239, a(38) = 347, a(40) = 2357, a(45) = 1579, a(58) = 25579, a(59) = 23459. Semiprimes include: a(4) = 4 = 2^2, a(10) = 158 = 2 * 79, a(11) = 339 = 3 * 113, a(16) = 178 = 2 * 89, a(19) = 146 = 2 * 73, a(22) = 3489 = 3 * 1163, a(23) = 689 = 13 * 53, a(31) = 1589 = 7 * 227, a(32) = 2369 = 23 * 103, a(33) = 11249 = 7 * 1607, a(35) = 2335 = 5 * 467, a(47) = 22789 = 13 * 1753, a(50) = 178999 = 19 * 9421, a(54) = 14567 = 7 * 2081, a(55) = 23469 = 3 * 7823, a(57) = 22467 = 3 * 7489, a(60) = 12499 = 29 * 431, a(63) = 1477 = 7 * 211, a(66) = 799 = 17 * 47.

Examples

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

Links

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

Crossrefs

Cf. A001592, A069638, A107281, A108564, A108565, 108567-108573.

Programs

Mathematica

nxt[{a_,b_,c_,d_,e_,f_}]:={b,c,d,e,f,FromDigits[Sort[IntegerDigits[Total[{a,b,c,d,e,f}]]]]}; NestList[nxt,{0,1,1,2,4,8},50][[All,1]] (* Harvey P. Dale, May 05 2022 *)

Formula

Sorted hexanacci numbers, a.k.a. sorted Fibonacci 6-step sequence.