%I #12 May 05 2022 13:43:30
%S 0,1,1,2,4,8,16,23,45,89,158,339,67,127,258,138,178,117,588,146,1245,
%T 1224,3489,689,1378,1178,239,1789,2678,1579,1488,1589,2369,11249,2259,
%U 2335,12289,239,347,12788,2357,3355,13357,23344,45558,1579,5589
%N 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.
%C 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.
%H Richard I. Hess, <a href="http://www.pme-math.org/journal/issues/PMEJ.Vol.10.No.9.pdf">Problem 920: sorted Fibonacci sequence</a>, Pi Mu Epsilon Journal, Vol. 10 (Fall 1998) No. 9, pp. 754-755.
%F Sorted hexanacci numbers, a.k.a. sorted Fibonacci 6-step sequence.
%e 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.
%t 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 *)
%Y Cf. A001592, A069638, A107281, A108564, A108565, 108567-108573.
%K base,easy,nonn
%O 0,4
%A _Jonathan Vos Post_, Jun 10 2005