A373234 -id:A373234 - cp's OEIS frontend

A274058 Relative of Hofstadter Q-sequence: a(n) = max(0, n+32478) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

6, 32479, 32480, 32481, 9, 32482, 32483, 32484, 12, 32485, 32486, 32487, 15, 32488, 32489, 17, 32491, 18, 32491, 32493, 32494, 22, 21, 64967, 64961, 9, 18, 64976, 64979, 32487, 22, 32508, 32513, 32491, 27, 36, 32515, 64966, 32482, 39, 32516, 32522

Offset: 1

Nathan Fox, Nov 10 2016

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 32478 terms.
This sequence has exactly 37025 terms (of positive index).  a(37025) = 0, so an attempt to calculate a(37026) would refer to itself.
Without the convention that a(n) = 0 for n <= -32478, this sequence would have exactly 24 terms (of positive index), since computing a(25) refers to a(-64942).
If 32478 in this sequence's definition is replaced by any larger number congruent to 5 mod 7, the behavior is essentially the same, though the quasilinear part (see Formula section) lasts longer.

Nathan Fox, Table of n, a(n) for n = 1..37025
N. Fox, Hofstadter-like Sequences over Nonstandard Integers", Talk given at the Rutgers Experimental Mathematics Seminar, November 10 2016.

Cf. A005185, A267501, A278055, A373234, A373235, A373236, A373237, A373238, A373239.

a[n_] := a[n] = If[n <= 0, Max[0, n + 2^15 - 290], a[n - a[n - 1]] + a[n - a[n - 2]] + a[n - a[n - 3]]]; Array[a, 42] (* Robert G. Wilson v, Mar 19 2017 *)

If the index is between 67 and 32479 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+32480, a(7n+2) = 7n+32482, a(7n+3) = 7, a(7n+4) = 2n+65001, a(7n+5) = n+64949, a(7n+6) = 32476.

Formula and definition corrected by Nathan Fox, Mar 18 2017

A373235 Relative of Hofstadter Q-sequence: a(n) = max(0, n+2087) 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, 2088, 2089, 2090, 9, 2091, 2092, 2093, 12, 2094, 2095, 2096, 15, 2097, 2098, 17, 2100, 18, 2100, 2102, 2103, 22, 21, 4185, 4179, 9, 18, 4194, 4197, 2096, 22, 2117, 2122, 2100, 27, 36, 2124, 4184, 2091, 39, 2125, 2131, 2095, 42, 2127, 2134, 16, 2126, 2134, 2114, 40, 2126, 55, 4198, 2103, 46, 2136, 2147, 25, 38, 58, 8399, 4188

Offset: 1

Nathan Fox, May 28 2024

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 2087 terms.
This sequence has exactly 2341 terms (of positive index).  a(2341) = 0, so an attempt to calculate a(2342) would refer to itself.
Without the convention that a(n) = 0 for n <= -2087, this sequence would have exactly 24 terms (of positive index), since computing a(25) refers to a(-4790).
If 2087 in this sequence's definition is replaced by any larger number congruent to 1 mod 7, the behavior is essentially the same, though the quasilinear part (see Formula section) lasts longer.

Nathan Fox, Table of n, a(n) for n = 1..2341

Cf. A005185, A267501, A278055, A373234, A373236, A373237, A373238, A274058, A373239.

If the index is between 67 and 2085 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+2089, a(7n+2) = 7n+2091, a(7n+3) = 7, a(7n+4) = 2n+4219, a(7n+5) = n+4167, a(7n+6) = 2085.

A373236 Relative of Hofstadter Q-sequence: a(n) = max(0, n+3201) 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, 3202, 3203, 3204, 9, 3205, 3206, 3207, 12, 3208, 3209, 3210, 15, 3211, 3212, 17, 3214, 18, 3214, 3216, 3217, 22, 21, 6413, 6407, 9, 18, 6422, 6425, 3210, 22, 3231, 3236, 3214, 27, 36, 3238, 6412, 3205, 39, 3239, 3245, 3209, 42, 3241, 3248, 16, 3240, 3248, 3228, 40, 3240, 55, 6426, 3217, 46, 3250, 3261, 25, 38, 58, 12855, 6416, 3205

Offset: 1

Nathan Fox, May 28 2024

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 3201 terms.
This sequence has exactly 3725 terms (of positive index).  a(3725) = 0, so an attempt to calculate a(3726) would refer to itself.
Without the convention that a(n) = 0 for n <= -3201, this sequence would have exactly 24 terms (of positive index), since computing a(25) refers to a(-6388).
If 3201 in this sequence's definition is replaced by any larger number congruent to 2 mod 7, the behavior is essentially the same, though the quasilinear part (see Formula section) lasts longer.

Nathan Fox, Table of n, a(n) for n = 1..3725

Cf. A005185, A267501, A278055, A373234, A373235, A373237, A373238, A274058, A373239.

If the index is between 67 and 3199 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+3203, a(7n+2) = 7n+3205, a(7n+3) = 7, a(7n+4) = 2n+6447, a(7n+5) = n+6395, a(7n+6) = 3199.

A373237 Relative of Hofstadter Q-sequence: a(n) = max(0, n+4315) 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, 4316, 4317, 4318, 9, 4319, 4320, 4321, 12, 4322, 4323, 4324, 15, 4325, 4326, 17, 4328, 18, 4328, 4330, 4331, 22, 21, 8641, 8635, 9, 18, 8650, 8653, 4324, 22, 4345, 4350, 4328, 27, 36, 4352, 8640, 4319, 39, 4353, 4359, 4323, 42, 4355, 4362, 16, 4354, 4362, 4342, 40, 4354, 55, 8654, 4331, 46, 4364, 4375, 25, 38, 58, 17311, 8644

Offset: 1

Nathan Fox, May 28 2024

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 4315 terms.
This sequence has exactly 4875 terms (of positive index).  a(4875) = 0, so an attempt to calculate a(4876) would refer to itself.
Without the convention that a(n) = 0 for n <= -4315, this sequence would have exactly 24 terms (of positive index), since computing a(25) refers to a(-8616).
If 4315 in this sequence's definition is replaced by any larger number congruent to 3 mod 7, the behavior is essentially the same, though the quasilinear part (see Formula section) lasts longer.

Nathan Fox, Table of n, a(n) for n = 1..4875

Cf. A005185, A267501, A278055, A373234, A373235, A373236, A373238, A274058, A373239.

If the index is between 67 and 4313 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+4317, a(7n+2) = 7n+4319, a(7n+3) = 7, a(7n+4) = 2n+8675, a(7n+5) = n+8623, a(7n+6) = 4313.

A373238 Relative of Hofstadter Q-sequence: a(n) = max(0, n+200) 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, 201, 202, 203, 9, 204, 205, 206, 12, 207, 208, 209, 15, 210, 211, 17, 213, 18, 213, 215, 216, 22, 21, 411, 405, 9, 18, 420, 423, 209, 22, 230, 235, 213, 27, 36, 237, 410, 204, 39, 238, 244, 208, 42, 240, 247, 16, 239, 247, 227, 40, 239, 55, 424, 216, 46, 249, 260, 25, 38, 58, 851, 414, 204, 61, 71, 463, 402, 198, 72, 272, 274

Offset: 1

Nathan Fox, May 28 2024

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 200 terms.
This sequence has exactly 220 terms (of positive index).  a(220) = 0, so an attempt to calculate a(221) would refer to itself.
Without the convention that a(n) = 0 for n <= -200, this sequence would have exactly 24 terms (of positive index), since computing a(25) refers to a(-386).
If 200 in this sequence's definition is replaced by any larger number congruent to 4 mod 7, the behavior is essentially the same, though the quasilinear part (see Formula section) lasts longer.

Nathan Fox, Table of n, a(n) for n = 1..220

Cf. A005185, A267501, A278055, A373234, A373235, A373236, A373237, A274058, A373239.

If the index is between 67 and 202 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+202, a(7n+2) = 7n+204, a(7n+3) = 7, a(7n+4) = 2n+445, a(7n+5) = n+393, a(7n+6) = 198.

A373239 Relative of Hofstadter Q-sequence: a(n) = max(0, n+118) 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, 119, 120, 121, 9, 122, 123, 124, 12, 125, 126, 127, 15, 128, 129, 17, 131, 18, 131, 133, 134, 22, 21, 247, 241, 9, 18, 256, 259, 127, 22, 148, 153, 131, 27, 36, 155, 246, 122, 39, 156, 162, 126, 42, 158, 165, 16, 157, 165, 145, 40, 157, 55, 260, 134, 46, 167, 178, 25, 38, 58, 523, 250, 122, 61, 71, 299, 238, 116, 72, 190, 192

Offset: 1

Nathan Fox, May 28 2024

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 118 terms.
This sequence has exactly 127 terms (of positive index). a(127) = 0, so an attempt to calculate a(128) would refer to itself.
Without the convention that a(n) = 0 for n <= -118, this sequence would have exactly 24 terms (of positive index), since computing a(25) refers to a(-222).
If 118 in this sequence's definition is replaced by any larger number congruent to 6 mod 7, the behavior is essentially the same, though the quasilinear part (see Formula section) lasts longer.

Nathan Fox, Table of n, a(n) for n = 1..127

Cf. A005185, A267501, A278055, A373234, A373235, A373236, A373237, A373238, A274058.

If the index is between 67 and 118 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+120, a(7n+2) = 7n+122, a(7n+3) = 7, a(7n+4) = 2n+281, a(7n+5) = n+229, a(7n+6) = 116.

cp's OEIS Frontend

A274058 Relative of Hofstadter Q-sequence: a(n) = max(0, n+32478) 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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A373235 Relative of Hofstadter Q-sequence: a(n) = max(0, n+2087) 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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A373236 Relative of Hofstadter Q-sequence: a(n) = max(0, n+3201) 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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A373237 Relative of Hofstadter Q-sequence: a(n) = max(0, n+4315) 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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A373238 Relative of Hofstadter Q-sequence: a(n) = max(0, n+200) 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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A373239 Relative of Hofstadter Q-sequence: a(n) = max(0, n+118) 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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