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

%I A277329 #11 Oct 30 2016 13:42:40
%S A277329 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,
%T A277329 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,
%U A277329 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
%N A277329 a(0)=0, for n >= 1, a(2n) = a(n)+1, a(4n-1) = a(n)+1, a(4n+1) = a(n)+1.
%C A277329 a(n) gives the index of the greatest prime dividing A260443(n).
%C A277329 Each n >= 1 occurs for the first time at 2^(n-1), which are also the positions of records.
%C A277329 For n >= 1, a(n) = number of terms in row n of A125184.
%F A277329 a(0)=0, for n >= 1, a(2n) = a(n)+1, a(4n-1) = a(n)+1, a(4n+1) = a(n)+1.
%F A277329 Other identities. For all n >= 0:
%F A277329 a(n) = A061395(A260443(n)).
%F A277329 a(2n+1) = max(a(n),a(n+1)).
%F A277329 For n >= 1, a(n) = 1+A057526(n).
%o A277329 (Scheme)
%o A277329 (define (A277329 n) (if (zero? n) n (+ 1 (A057526 n)))) ;; Code for A057526 given in that entry.
%o A277329 ;; Standalone recurrence:
%o A277329 (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))))))
%Y A277329 One more than A057526.
%Y A277329 Cf. A061395, A125184, A260443.
%K A277329 nonn
%O A277329 0,3
%A A277329 _Antti Karttunen_, Oct 27 2016