A283885 -id:A283885 - cp's OEIS frontend

A283884 Relative of Hofstadter Q-sequence: a(n) = max(0, n+193) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

6, 194, 195, 196, 9, 197, 198, 199, 12, 200, 201, 202, 15, 203, 204, 17, 206, 18, 206, 208, 209, 22, 21, 397, 391, 9, 18, 406, 409, 202, 22, 223, 228, 206, 27, 36, 230, 396, 197, 39, 231, 237, 201, 42, 233, 240, 16, 232, 240, 220, 40

Offset: 1

Nathan Fox, Mar 19 2017

Sequences like this are more naturally considered with the first nonzero term in position 1. But this sequence would then match A000027 for its first 193 terms.

Most terms in this sequence appear in long period-5 quasilinear runs. These runs are separated by 441 other terms, and each run is approximately six times as long as the previous.

Nathan Fox, Table of n, a(n) for n = 1..10000

Cf. A005185, A267501, A274058, A278055, A278066, A283885, A283886, A283887, A283888.

A283884:=proc(n) option remember: if n <= 0 then max(0, n+193): else A283884(n-A283884(n-1)) + A283884(n-A283884(n-2)) + A283884(n-A283884(n-3)): fi: end:

If the index is between 67 and 195 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+195, a(7n+2) = 7n+197, a(7n+3) = 7, a(7n+4) = 2n+431, a(7n+5) = n+379, a(7n+6) = 191.
For nonnegative integers i, if 1<=5n+r<=(2417/5)*6^(i+1)-3382/5, then
a((2417/5)*6^i-1177/5+5n) = 5
a((2417/5)*6^i-1177/5+5n+1) = (7251/5)*6^i - 2046/5 + 3n
a((2417/5)*6^i-1177/5+5n+2) = 3
a((2417/5)*6^i-1177/5+5n+3) = (2417/5)*6^i - 1162/5 + 5n
a((2417/5)*6^i-1177/5+5n+4) = (7251/5)*6^i - 2041/5 + 3n.

A283886 Relative of Hofstadter Q-sequence: a(n) = max(0, n+19395) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

Original entry on oeis.org

6, 19396, 19397, 19398, 9, 19399, 19400, 19401, 12, 19402, 19403, 19404, 15, 19405, 19406, 17, 19408, 18, 19408, 19410, 19411, 22, 21, 38801, 38795, 9, 18, 38810, 38813, 19404, 22, 19425, 19430, 19408, 27, 36, 19432, 38800, 19399, 39

Offset: 1

Nathan Fox, Mar 19 2017

Sequences like this are more naturally considered with the first nonzero term in position 1. But this sequence would then match A000027 for its first 19395 terms.
Most terms in this sequence appear in a long pattern stretching from a(58340) through a(80425266), of 16 interleaved sequences.
This sequence has exactly 80425397 terms (of positive index). a(80425397) = 0, so an attempt to calculate a(80425398) would refer to itself.

Nathan Fox, Table of n, a(n) for n = 1..61000

Cf. A005185, A267501, A274058, A278055, A278066, A283884, A283885, A283887, A283888.

A283886:=proc(n) option remember: if n <= 0 then max(0, n+19395): else A283886(n-A283886(n-1)) + A283886(n-A283886(n-2)) + A283886(n-A283886(n-3)): fi: end:

If the index is between 67 and 19396 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+19397, a(7n+2) = 7n+19399, a(7n+3) = 7, a(7n+4) = 2n+38835, a(7n+5) = n+38783, a(7n+6) = 19393.

A283887 Relative of Hofstadter Q-sequence: a(n) = max(0, n+20830) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

Original entry on oeis.org

6, 20831, 20832, 20833, 9, 20834, 20835, 20836, 12, 20837, 20838, 20839, 15, 20840, 20841, 17, 20843, 18, 20843, 20845, 20846, 22, 21, 41671, 41665, 9, 18, 41680, 41683, 20839, 22, 20860, 20865, 20843, 27, 36, 20867, 41670, 20834, 39

Offset: 1

Nathan Fox, Mar 19 2017

Sequences like this are more naturally considered with the first nonzero term in position 1. But this sequence would then match A000027 for its first 20830 terms.
Most terms in this sequence appear in one of two long patterns of 16 interleaved sequences. The first stretches from a(64180) through a(9029945). The second stretches from a(9029971) through a(-20830 + 84975*2^560362).
This sequence has exactly -20799 + 84975*2^560362 terms (of positive index). a(-20799 + 84975*2^560362) = 0, so an attempt to calculate a(-20798 + 84975*2^560362) would refer to itself.

Nathan Fox, Table of n, a(n) for n = 1..68000

Cf. A005185, A267501, A274058, A278055, A278066, A283884, A283885, A283886, A283888.

A283887:=proc(n) option remember: if n <= 0 then max(0, n+20830): else A283887(n-A283887(n-1)) + A283887(n-A283887(n-2)) + A283887(n-A283887(n-3)): fi: end:

If the index is between 67 and 20831 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+20832, a(7n+2) = 7n+20834, a(7n+3) = 7, a(7n+4) = 2n+41705, a(7n+5) = n+41653, a(7n+6) = 20828.

A283888 Relative of Hofstadter Q-sequence: a(n) = max(0, n+27298) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

Original entry on oeis.org

6, 27299, 27300, 27301, 9, 27302, 27303, 27304, 12, 27305, 27306, 27307, 15, 27308, 27309, 17, 27311, 18, 27311, 27313, 27314, 22, 21, 54607, 54601, 9, 18, 54616, 54619, 27307, 22, 27328, 27333, 27311, 27, 36, 27335, 54606, 27302, 39

Offset: 1

Nathan Fox, Mar 19 2017

Sequences like this are more naturally considered with the first nonzero term in position 1. But this sequence would then match A000027 for its first 27298 terms.
Most terms in this sequence appear in a long pattern stretching from a(85652) through a(141867984), of 16 interleaved sequences.
This sequence has exactly 141868181 terms (of positive index). a(141868181) = 0, so an attempt to calculate a(141868182) would refer to itself.

Nathan Fox, Table of n, a(n) for n = 1..90000

Cf. A005185, A267501, A274058, A278055, A278066, A283884, A283885, A283886, A283887.

A283888:=proc(n) option remember: if n <= 0 then max(0, n+27298): else A283888(n-A283888(n-1)) + A283888(n-A283888(n-2)) + A283888(n-A283888(n-3)): fi: end:

If the index is between 67 and 27299 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+27300, a(7n+2) = 7n+27302, a(7n+3) = 7, a(7n+4) = 2n+54641, a(7n+5) = n+54589, a(7n+6) = 27296.

cp's OEIS Frontend

A283884 Relative of Hofstadter Q-sequence: a(n) = max(0, n+193) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

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A283886 Relative of Hofstadter Q-sequence: a(n) = max(0, n+19395) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

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A283887 Relative of Hofstadter Q-sequence: a(n) = max(0, n+20830) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

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Programs

Maple

Formula

A283888 Relative of Hofstadter Q-sequence: a(n) = max(0, n+27298) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

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Comments

Links

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Programs

Maple

Formula