A108566 -id:A108566 - cp's OEIS frontend

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

Jonathan Vos Post, Jun 10 2005

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.

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

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.

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

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]]

A370254 a(0) = 1, a(n) = result of eliminating the digit 7 from the sum of all previous terms for n>=1.

Original entry on oeis.org

1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 3268, 36036, 202, 224, 2498, 4996, 9992, 89984, 19968, 199936, 39982, 439854, 8908, 888616, 1232, 18464, 196928, 1993856, 39812, 402524, 4430048, 8860096, 120192, 1840384, 1968068

Offset: 0

Sergio Pimentel, Feb 13 2024

			a(16) = 3268 since the sum of a(0)..a(15) = 32768. Eliminating the "7" we get 3268.

Alois P. Heinz, Table of n, a(n) for n = 0..16384

Cf. A004182, A011782, A069638, A108566.

a:= proc(n) option remember; `if`(n=0, 1, (l-> add(l[i]*10^(i-1),
      i=1..nops(l)))(subs(7=NULL, convert(s(n-1), base, 10))))
    end:
s:= proc(n) option remember; `if`(n<0, 0, s(n-1)+a(n)) end:
seq(a(n), n=0..40);  # Alois P. Heinz, Feb 15 2024

Module[{nmax=50, s=1, a}, NestList[(s+=(a=FromDigits[DeleteCases[IntegerDigits[s], 7]]); a) &, s, nmax]] (* Paolo Xausa, Feb 19 2024 *)

lista(nn) = my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = sum(k=1, n-1, va[k]); my(d=digits(va[n])); if (vecsearch(Set(d), 7), my(list = List()); for (i=1, #d, if (d[i] !=7, listput(list, d[i]));); va[n] = fromdigits(Vec(list)););); va; \\ Michel Marcus, Feb 13 2024

a(n) = A004182(Sum_{i=0..n-1} a(i)) for n >= 1, a(0) = 1.

a(n) = A011782(n) for n <= 15.

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.

Original entry on oeis.org

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

Jonathan Vos Post, Jun 11 2005

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.

			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.

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.

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

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 *)

cp's OEIS Frontend

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.

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A370254 a(0) = 1, a(n) = result of eliminating the digit 7 from the sum of all previous terms for n>=1.

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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.

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Mathematica