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.

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

Author

Nathan Fox, May 28 2024

Keywords

• nonn

Comments

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.

Links

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

Crossrefs

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.

Programs

Mathematica

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 *)