A278056 -id:A278056 - cp's OEIS frontend

A373228 Relative of Hofstadter Q-sequence: a(n) = n for 1 <= n <= 8; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 8.

1, 2, 3, 4, 5, 6, 7, 8, 6, 9, 10, 11, 9, 12, 13, 14, 12, 15, 16, 17, 15, 18, 19, 17, 21, 18, 21, 23, 24, 19, 26, 23, 28, 24, 28, 27, 24, 31, 32, 28, 24, 36, 36, 33, 23, 37, 38, 40, 27, 39, 38, 42, 35, 41, 38, 43, 42, 44, 39, 44, 42, 51, 42, 45, 48, 47, 51, 44, 54, 48, 52, 49, 53

Offset: 1

Nathan Fox, May 28 2024

nonn

Similar to A278055 but with different starting values.
Much like the Hofstadter Q-sequence A005185, it is not known if this sequence is defined for all positive n.
a(n) exists for n <= 3*10^7.

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

Cf. A005185, A278055, A373227, A373229, A373230, A373231, A373232, A373233.

Similar sequences based on the Q-recurrence: A278056, A278057, A278058, A278059, A278060, A278061, A278062, A278063, A278064, A278065.

a[n_] := a[n] = If[0 < n < 9, n, a[n-a[n-1]] + a[n-a[n-2]] + a[n-a[n-3]]];
Array[a, 100] (* Paolo Xausa, May 31 2024 *)

A373229 Relative of Hofstadter Q-sequence: a(n) = n for 1 <= n <= 9; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 9.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 6, 10, 11, 12, 9, 13, 14, 15, 12, 16, 17, 18, 15, 19, 20, 17, 22, 18, 22, 24, 25, 22, 21, 29, 28, 22, 24, 34, 27, 29, 28, 32, 27, 37, 33, 31, 34, 35, 36, 34, 36, 41, 36, 41, 36, 41, 43, 41, 43, 40, 48, 42, 41, 46, 46, 52, 43, 51, 46, 53, 51, 46, 56, 48

Offset: 1

Nathan Fox, May 28 2024

nonn

Similar to A278055 but with different starting values.
Much like the Hofstadter Q-sequence A005185, it is not known if this sequence is defined for all positive n.
a(n) exists for n <= 3*10^7.

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

Cf. A005185, A278055, A373227, A373228, A373230, A373231, A373232, A373233.

Similar sequences based on the Q-recurrence: A278056, A278057, A278058, A278059, A278060, A278061, A278062, A278063, A278064, A278065.

a[n_] := a[n] = If[0 < n < 10, n, a[n-a[n-1]] + a[n-a[n-2]] + a[n-a[n-3]]];
Array[a, 100] (* Paolo Xausa, May 31 2024 *)

A373230 Relative of Hofstadter Q-sequence: a(n) = 0 for n <= 0, a(n) = n for 1 <= n <= 10; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 10.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 6, 11, 12, 13, 9, 14, 15, 16, 12, 17, 18, 19, 15, 20, 21, 17, 23, 18, 23, 25, 26, 22, 21, 31, 29, 21, 28, 34, 27, 29, 31, 27, 38, 33, 34, 31, 39, 37, 37, 30, 44, 36, 39, 35, 43, 45, 43, 30, 50, 50, 38, 42, 51, 48, 43, 40, 55, 51, 52, 37, 60, 57, 47

Offset: 1

Nathan Fox, May 28 2024

nonn

Similar to A278055 but with different starting values.
a(1015) = 1036. This is the smallest index for which a(n) > n. So, without the condition that a(n) = 0 for n <= 0, this sequence would be finite and have exactly 1015 terms.
Much like the Hofstadter Q-sequence A005185, it is not known if this sequence is defined for all positive n.
a(n) exists for n <= 3*10^7.

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

Cf. A005185, A278055, A373227, A373228, A373229, A373231, A373232, A373233.

Similar sequences based on the Q-recurrence: A278056, A278057, A278058, A278059, A278060, A278061, A278062, A278063, A278064, A278065.

a[n_] := a[n] = Which[n < 1, 0, n < 11, n, True, a[n-a[n-1]] + a[n-a[n-2]] + a[n-a[n-3]]]; Array[a, 100] (* Paolo Xausa, May 31 2024 *)

A373231 Relative of Hofstadter Q-sequence: a(n) = 0 for n <= 0, a(n) = n for 1 <= n <= 11; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 11.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 6, 12, 13, 14, 9, 15, 16, 17, 12, 18, 19, 20, 15, 21, 22, 17, 24, 18, 24, 26, 27, 22, 21, 33, 30, 20, 29, 36, 27, 24, 36, 33, 31, 28, 42, 31, 33, 32, 48, 36, 25, 44, 44, 46, 22, 56, 38, 41, 40, 50, 43, 44, 43, 56, 49, 42, 45, 44, 67, 43, 47, 52

Offset: 1

Nathan Fox, May 28 2024

nonn

Similar to A278055 but with different starting values.
a(117) = 120. This is the smallest index for which a(n) > n. So, without the condition that a(n) = 0 for n <= 0, this sequence would be finite and have exactly 117 terms.
Much like the Hofstadter Q-sequence A005185, it is not known if this sequence is defined for all positive n.
a(n) exists for n <= 3*10^7.

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

Cf. A005185, A278055, A373227, A373228, A373229, A373230, A373232, A373233.

Similar sequences based on the Q-recurrence: A278056, A278057, A278058, A278059, A278060, A278061, A278062, A278063, A278064, A278065.

a[n_] := a[n] = Which[n < 1, 0, n < 12, n, True, a[n-a[n-1]] + a[n-a[n-2]] + a[n-a[n-3]]]; Array[a, 100] (* Paolo Xausa, May 31 2024 *)

A373232 Relative of Hofstadter Q-sequence: a(n) = 0 for n <= 0, a(n) = n for 1 <= n <= 12; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 12.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 6, 13, 14, 15, 9, 16, 17, 18, 12, 19, 20, 21, 15, 22, 23, 17, 25, 18, 25, 27, 28, 22, 21, 35, 31, 19, 30, 31, 40, 25, 31, 27, 47, 31, 33, 24, 46, 35, 43, 24, 51, 32, 49, 33, 44, 37, 55, 40, 39, 46, 50, 44, 43, 54, 47, 40, 58, 50, 43, 57, 53

Offset: 1

Nathan Fox, May 28 2024

nonn

Similar to A278055 but with different starting values.
a(45) = 47. This is the smallest index for which a(n) > n. So, without the condition that a(n) = 0 for n <= 0, this sequence would be finite and have exactly 45 terms.
Much like the Hofstadter Q-sequence A005185, it is not known if this sequence is defined for all positive n.
a(n) exists for n <= 3*10^7.

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

Cf. A005185, A278055, A373227, A373228, A373229, A373230, A373231, A373233.

Similar sequences based on the Q-recurrence: A278056, A278057, A278058, A278059, A278060, A278061, A278062, A278063, A278064, A278065.

a[n_] := a[n] = Which[n < 1, 0, n < 13, n, True, a[n-a[n-1]] + a[n-a[n-2]] + a[n-a[n-3]]]; Array[a, 100] (* Paolo Xausa, May 31 2024 *)

A373233 Relative of Hofstadter Q-sequence: a(n) = 0 for n <= 0, a(n) = n for 1 <= n <= 13; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 13.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 6, 14, 15, 16, 9, 17, 18, 19, 12, 20, 21, 22, 15, 23, 24, 17, 26, 18, 26, 28, 29, 22, 21, 37, 32, 18, 23, 38, 42, 24, 26, 39, 37, 37, 31, 33, 46, 32, 41, 38, 40, 36, 42, 49, 36, 46, 38, 56, 42, 48, 35, 62, 31, 52, 58, 59, 32, 43, 53, 82

Offset: 1

Nathan Fox, May 28 2024

nonn

Similar to A278055 but with different starting values.
a(73) = 82. This is the smallest index for which a(n) > n. So, without the condition that a(n) = 0 for n <= 0, this sequence would be finite and have exactly 73 terms.
Much like the Hofstadter Q-sequence A005185, it is not known if this sequence is defined for all positive n.
a(n) exists for n <= 3*10^7.

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

Cf. A005185, A278055, A373227, A373228, A373229, A373230, A373231, A373232.

Similar sequences based on the Q-recurrence: A278056, A278057, A278058, A278059, A278060, A278061, A278062, A278063, A278064, A278065.

a[n_] := a[n] = Which[n < 1, 0, n < 14, n, True, a[n-a[n-1]] + a[n-a[n-2]] + a[n-a[n-3]]]; Array[a, 100] (* Paolo Xausa, May 31 2024 *)

A274055 Relative of Hofstadter Q-sequence: a(n) = n for 1 <= n <= 42; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 42.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 3, 43, 44, 5, 45, 6, 7, 46, 48, 10, 8, 48, 52, 12, 49, 14, 54, 11, 53, 57, 16, 13, 17, 15, 56, 20, 20

Offset: 1

Nathan Fox, Nov 13 2016

nonn

In calculating terms of this sequence, use the convention that a(n)=0 for n<=0.

This sequence eventually settles into a pattern resembling A272610.

Nathan Fox, Table of n, a(n) for n = 1..40000
N. Fox, Hofstadter-like Sequences over Nonstandard Integers", Talk given at the Rutgers Experimental Mathematics Seminar, November 10 2016.

Cf. A005185, A272610, A272611, A272612, A272613, A278056, A278057, A278058, A278059, A278060, A278061, A278062, A278063, A278064, A278065.

If the index is between 77 and 89 (inclusive), then a(5n) = 3, a(5n+1) = 5, a(5n+2) = 88n-1188, a(5n+3) = 5, a(5n+4) = 88.
If the index is between 95 and 397 (inclusive), then a(5n) = 396n-6820, a(5n+1) = 3, a(5n+2) = 396, a(5n+3) = 3, a(5n+4) = 5.
If the index is between 403 and 24860 (inclusive), then a(5n) = 24860, a(5n+1) = 3, a(5n+2) = 5, a(5n+3) = 24860n-1939476, a(5n+4) = 5.
If the index is at least 24863, then a(5n) = 24860*A272613(n-4972), a(5n+1) = 4, a(5n+2) = 5*A272611(n-4972), a(5n+3) = 5*A272611(n-4971), a(5n+4) = 5*A272612(n-4971). This pattern lasts as long as A272611 exists (which is conjectured to be forever).

cp's OEIS Frontend

A373228 Relative of Hofstadter Q-sequence: a(n) = n for 1 <= n <= 8; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 8.

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A373229 Relative of Hofstadter Q-sequence: a(n) = n for 1 <= n <= 9; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 9.

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A373230 Relative of Hofstadter Q-sequence: a(n) = 0 for n <= 0, a(n) = n for 1 <= n <= 10; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 10.

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A373231 Relative of Hofstadter Q-sequence: a(n) = 0 for n <= 0, a(n) = n for 1 <= n <= 11; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 11.

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A373232 Relative of Hofstadter Q-sequence: a(n) = 0 for n <= 0, a(n) = n for 1 <= n <= 12; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 12.

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A373233 Relative of Hofstadter Q-sequence: a(n) = 0 for n <= 0, a(n) = n for 1 <= n <= 13; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 13.

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A274055 Relative of Hofstadter Q-sequence: a(n) = n for 1 <= n <= 42; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 42.

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