A108565 - OEIS

%I #14 May 16 2019 14:57:10

%S 0,1,1,2,4,8,16,13,34,57,128,248,48,155,366,459,1267,2259,456,478,

%T 1499,5599,1129,1169,4789,11458,12444,3899,33579,16669,4789,1378,1346,

%U 15677,35899,5899,1699,256,3459,12247,2356,127,14458,23467,25556,45669,12779

%N 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.

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

%C 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.

%H Harvey P. Dale, <a href="/A108565/b108565.txt">Table of n, a(n) for n = 0..1000</a>

%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.

%e a(8) = SORT[a(3) + a(4) + a(5) + a(6) + a(7)] = SORT[61] = 16.

%t 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]]

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

%K base,easy,nonn

%O 0,4

%A _Jonathan Vos Post_, Jun 10 2005