A283472 a(n) = A004001(A004001(n-1)) AND A004001(n-A004001(n-1)), a(1) = a(2) = 0.

0, 0, 1, 1, 0, 2, 2, 2, 2, 3, 0, 0, 4, 4, 4, 4, 4, 5, 4, 5, 5, 6, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 9, 8, 9, 8, 8, 8, 8, 10, 10, 10, 11, 11, 12, 12, 12, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 16, 16, 16, 16, 16, 16, 17, 16, 17, 16, 17, 17, 16, 18, 18, 16, 16, 16, 17, 18, 18, 16, 16, 16, 17, 17, 17, 18, 20, 20, 20, 21, 22, 22, 24, 24, 24, 24

Offset: 1

Author

Antti Karttunen, Mar 18 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A004001, A004198, A283469, A283470, A283473 (positions of zeros).

Programs

Mathematica

a[n_] := a[n] = If[n <= 2, 1, a[a[n - 1]] + a[n - a[n - 1]]]; Table[BitAnd[a[#], a[n - #]] &@ a[n - 1] - Boole[n <= 2], {n, 97}] (* Michael De Vlieger, Mar 18 2017, after Robert G. Wilson v at A004001 *)

Scheme

(define (A283472 n) (if (<= n 2) 0 (A004198bi (A004001 (A004001 (- n 1))) (A004001 (- n (A004001 (- n 1)))))))
;; A004198bi implements bitwise-AND (see A004198). Code for A004001 given under that entry.

Formula

a(1) = a(2) = 0; for n > 2, a(n) = A004001(A004001(n-1)) AND A004001(A080677(n-1)), where AND is bitwise-and (A004198).

Other identities. For all n >= 1:

a(n) = A283469(n) - A283470(n).

A004001(n) = A283469(n) + a(n) = A283470(n) + 2*a(n).