A278061 Relative of Hofstadter Q-sequence: a(n) = n for 1 <= n <= 9; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 9.

1, 2, 3, 4, 5, 6, 7, 8, 9, 3, 10, 11, 5, 12, 6, 7, 13, 15, 10, 8, 15, 19, 12, 16, 14, 14, 10, 27, 12, 18, 15, 25, 23, 19, 18, 28, 19, 13, 22, 25, 17, 27, 21, 25, 24, 34, 17, 27, 44, 18, 30, 38, 18, 35, 27, 27, 36, 34, 26, 33, 45, 25, 28, 50

Offset: 1

Author

Nathan Fox, Nov 10 2016

Keywords

• nonn

Comments

Similar to Hofstadter's Q-sequence A005185 but with different starting values.

Much like the Hofstadter Q-sequence, 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
• Nathan Fox, Hofstadter-like Sequences over Nonstandard Integers, Talk given at the Rutgers Experimental Mathematics Seminar, November 10 2016.

Crossrefs

Cf. A005185, A278056, A278057, A278058, A278059, A278060, A278062, A278063, A278064, A278065.

Programs

Magma

[n le 9 select n else Self(n-Self(n-1))+Self(n-Self(n-2)): n in [1..70]]; // Bruno Berselli, Nov 15 2016

Mathematica

a[n_] := a[n] = If[0 < n < 10, n, a[n-a[n-1]] + a[n-a[n-2]]];
Array[a, 100] (* Paolo Xausa, May 29 2024 *)