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Relative of Hofstadter Q-sequence: a(n) = n for 1 <= n <= 7; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 7.
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7
1, 2, 3, 4, 5, 6, 7, 6, 8, 9, 10, 9, 11, 12, 13, 12, 14, 15, 16, 15, 17, 18, 17, 20, 18, 20, 22, 21, 21, 22, 26, 25, 23, 24, 28, 26, 29, 26, 31, 30, 32, 28, 34, 30, 37, 29, 38, 35, 37, 33, 39, 40, 38, 37, 42, 43, 40, 40, 44, 42, 47, 43, 44, 46, 51, 46, 46, 50, 50, 50, 51, 53, 50
COMMENTS
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.
MATHEMATICA
a[n_] := a[n] = If[0 < n < 8, n, a[n-a[n-1]] + a[n-a[n-2]] + a[n-a[n-3]]];
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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7
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
COMMENTS
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.
MATHEMATICA
a[n_] := a[n] = If[0 < n < 9, n, a[n-a[n-1]] + a[n-a[n-2]] + a[n-a[n-3]]];
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.
+10
7
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
COMMENTS
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.
MATHEMATICA
a[n_] := a[n] = If[0 < n < 10, n, a[n-a[n-1]] + a[n-a[n-2]] + a[n-a[n-3]]];
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.
+10
7
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
COMMENTS
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.
MATHEMATICA
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 *)
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.
+10
7
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
COMMENTS
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.
MATHEMATICA
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 *)
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.
+10
7
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
COMMENTS
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.
MATHEMATICA
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 *)
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