A107281 -id:A107281 - cp's OEIS frontend

A108564 a(0) = 0, a(1) = 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)], where SORT places digits in ascending order and deletes 0's.

0, 1, 1, 2, 4, 8, 15, 29, 56, 18, 118, 122, 134, 239, 136, 136, 456, 679, 147, 1148, 234, 228, 1577, 1378, 1347, 345, 4467, 3577, 3679, 1268, 11299, 12389, 23568, 24458, 11477, 12789, 22279, 137, 24668, 35789, 23788, 23488, 13377, 24469, 12258, 23579

Offset: 0

Jonathan Vos Post, Jun 10 2005

Sorted tetranacci numbers, a.k.a. sorted Fibonacci 4-step sequence.

As found by T. D. Noe: Max=4556699. Cycle period=41652. Cycle starts with the 23944th term.

			a(8) = SORT[a(4) + a(5) + a(6) + a(7)] = SORT[108] = 18.
a(10) = SORT[a(6) + a(7) + a(8) + a(9)] = SORT[221] = 122.

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. A000078, A069638, A107281, A108565-A108573.

nxt[{a_,b_,c_,d_,e_}]:={b,c,d,e,FromDigits[Sort[DeleteCases[ IntegerDigits[ b+c+d+e],?0]]]}; NestList[nxt,{0,1,1,2,4},50][[All,1]] (* _Harvey P. Dale, Jan 17 2022 *)

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.

Original entry on oeis.org

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]]

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.

Original entry on oeis.org

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

Jonathan Vos Post, Jun 10 2005

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.

			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.

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

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

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 *)

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

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

A108564 a(0) = 0, a(1) = 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)], where SORT places digits in ascending order and deletes 0's.

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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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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.

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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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