A116592 a(0)=1; a(n) = b(n+2) + b(n), where b(n) = A004001(n) is the Hofstadter-Conway sequence defined by b(1) = b(2) = 1, b(n) = b(b(n-1)) + b(n-b(n-1)) for n>2.

1, 3, 3, 5, 6, 7, 8, 9, 10, 12, 13, 15, 15, 16, 16, 17, 18, 20, 22, 23, 25, 26, 27, 29, 29, 30, 31, 31, 32, 32, 32, 33, 34, 36, 38, 40, 41, 43, 44, 46, 47, 49, 50, 51, 53, 53, 54, 55, 56, 57, 59, 59, 60, 61, 61, 62, 62, 63, 63, 64, 64, 64, 64, 65, 66, 68, 70, 72, 74, 75, 77, 78

Offset: 0

Author

Roger L. Bagula, Mar 27 2006

Keywords

• nonn

Comments

A similar definition applied to the Fibonacci sequence (A000045) leads to the Lucas sequence (A000032).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A000032, A005185, A005229, A004001.

Programs

Maple

b:=proc(n) option remember; if n<=2 then 1 else b(b(n-1))+b(n-b(n-1)): fi: end: seq(b(n),n=1..71): a:=proc(n) if n=0 then 1 else b(n+2)+b(n) fi end: seq(a(n),n=0..71);

Mathematica

Cw[0] = 0; Cw[1] = Cw[2] = 1; Cw[n_Integer?Positive] := Cw[n] = Cw[Cw[n - 1]] + Cw[n - Cw[n - 1]]; L[0] = 1; L[n_] := L[n] = Cw[n - 1] + Cw[n + 1]; Table[L[n], {n, 1, 200}]

Formula

a(n) = A004001(n+2) + A004001(n) for n>=1.

Extensions

Edited by N. J. A. Sloane, Apr 15 2006