A277329 a(0)=0, for n >= 1, a(2n) = a(n)+1, a(4n-1) = a(n)+1, a(4n+1) = a(n)+1.

0, 1, 2, 2, 3, 2, 3, 3, 4, 3, 3, 3, 4, 3, 4, 4, 5, 4, 4, 3, 4, 3, 4, 4, 5, 4, 4, 4, 5, 4, 5, 5, 6, 5, 5, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4, 5, 5, 6, 5, 5, 4, 5, 4, 5, 5, 6, 5, 5, 5, 6, 5, 6, 6, 7, 6, 6, 5, 6, 5, 5, 5, 6, 5, 5, 4, 5, 4, 5, 5, 6, 5, 5, 4, 5, 4, 5, 5, 6, 5, 5, 5, 6, 5, 6, 6, 7, 6, 6, 5, 6, 5, 5, 5, 6, 5, 5, 5, 6, 5, 6, 6, 7, 6, 6, 5, 6, 5, 6, 6, 7

Offset: 0

Author

Antti Karttunen, Oct 27 2016

Keywords

• nonn

Comments

a(n) gives the index of the greatest prime dividing A260443(n).

Each n >= 1 occurs for the first time at 2^(n-1), which are also the positions of records.

For n >= 1, a(n) = number of terms in row n of A125184.

Crossrefs

One more than A057526.

Cf. A061395, A125184, A260443.

Programs

Scheme

(define (A277329 n) (if (zero? n) n (+ 1 (A057526 n)))) ;; Code for A057526 given in that entry.
;; Standalone recurrence:
(definec (A277329 n) (cond ((zero? n) n) ((even? n) (+ 1 (A277329 (/ n 2)))) ((= 3 (modulo n 4)) (+ 1 (A277329 (/ (+ 1 n) 4)))) (else (+ 1 (A277329 (/ (+ -1 n) 4))))))

Formula

a(0)=0, for n >= 1, a(2n) = a(n)+1, a(4n-1) = a(n)+1, a(4n+1) = a(n)+1.

Other identities. For all n >= 0:

a(n) = A061395(A260443(n)).

a(2n+1) = max(a(n),a(n+1)).

For n >= 1, a(n) = 1+A057526(n).