A274058 -id:A274058 - cp's OEIS frontend

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.

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.

A283883 Relative of Hofstadter Q-sequence: a(n) = max(0, n+117) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 0.

Original entry on oeis.org

3, 118, 119, 5, 120, 6, 7, 121, 123, 10, 8, 123, 127, 12, 124, 14, 129, 11, 128, 132, 16, 13, 17, 15, 131, 20, 20, 242, 123, 24, 32, 238, 3, 32, 357, 5, 238, 3, 5, 595, 5, 238, 3, 5, 833, 5, 238, 3, 5, 1071, 5, 238, 3, 5, 1309, 5, 238, 3, 5, 1547, 5, 238, 3, 5, 1785, 5, 238, 3, 5, 2023, 5, 238, 3, 5, 2261

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 117 terms.

This sequence has exactly 3346939303954 terms (of positive index). a(3346939303954) = 0, so an attempt to calculate a(3346939303955) would refer to itself.

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

Cf. A005185, A274058, A283883.

A283883:=proc(n) option remember: if n <= 0 then max(0, n+117): else A283883(n-A283883(n-1)) + A283883(n-A283883(n-2)): fi: end:

If the index is between 35 and 122 (inclusive), then a(5n) = 238n-1309, a(5n+1) = 5, a(5n+2) = 238, a(5n+3) = 3, a(5n+4) = 5.
If the index is between 128 and 4525 (inclusive), then a(5n) = 4641, a(5n+1) = 3, a(5n+2) = 5, a(5n+3) = 4641n-106981, a(5n+4) = 5.
If the index is between 4531 and 4093008 (inclusive), then a(5n) = 5, a(5n+1) = 4093124n-3700188737, a(5n+2) = 5, a(5n+3) = 4093124, a(5n+4) = 3.
If the index is between 4093008 and 3346939303796 (inclusive), then a(5n) = 5, a(5n+1) = 3346939303911, a(5n+2) = 3, a(5n+3) = 5, a(5n+4) = 3346939303911n-2739804514185637724.

A283882 Relative of Hofstadter Q-sequence: a(n) = max(0, n+67) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 0.

Original entry on oeis.org

3, 68, 69, 5, 70, 6, 7, 71, 73, 10, 8, 73, 77, 12, 74, 14, 79, 11, 78, 82, 16, 13, 17, 15, 81, 20, 20, 142, 73, 24, 32, 138, 3, 32, 207, 5, 138, 3, 5, 345, 5, 138, 3, 5, 483, 5, 138, 3, 5, 621, 5, 138, 3, 5, 759, 5, 138, 3, 5, 897, 5, 138, 3, 5, 1035, 5, 138, 3, 5, 1173, 5, 138, 5, 8, 1311

Offset: 1

Nathan Fox, Mar 19 2017

nonn

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 67 terms.

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

Cf. A005185, A272610, A272611, A272612, A272613, A274058, A283883.

A283882:=proc(n) option remember: if n <= 0 then max(0, n+67): else A283882(n-A283882(n-1)) + A283882(n-A283882(n-2)): fi: end:

If the index is between 35 and 72 (inclusive), then a(5n) = 138n-759, a(5n+1) = 5, a(5n+2) = 138, a(5n+3) = 3, a(5n+4) = 5.
If the index is between 78 and 1245 (inclusive), then a(5n) = 1311, a(5n+1) = 3, a(5n+2) = 5, a(5n+3) = 1311n-17181, a(5n+4) = 5.
If the index is between 1251 and 309192 (inclusive), then a(5n) = 5, a(5n+1) = 19047817435n-1178393232110703, a(5n+2) = 5, a(5n+3) = 19047817435, a(5n+4) = 3.
If the index is between 309336 and 19047817368 (inclusive), then a(5n) = 5, a(5n+1) = 309258n-76697295, a(5n+2) = 5, a(5n+3) = 309258, a(5n+4) = 3.
If the index is at least 19047817371, then a(5n) = 5*A272611(n-3809563474), a(5n+1) = 5*A272611(n-3809563473), a(5n+2) = 5*A272612(n-3809563473), a(5n+3) = 19047817435*A272613(n-3809563473), a(5n+4) = 4. This pattern lasts as long as A272611 exists (which is conjectured to be forever).

cp's OEIS Frontend

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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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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A283883 Relative of Hofstadter Q-sequence: a(n) = max(0, n+117) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 0.

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A283882 Relative of Hofstadter Q-sequence: a(n) = max(0, n+67) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 0.

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