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A096115 If n = (2^k)-1, a(n) = a((n+1)/2) = k, if n = 2^k, a(n) = a(n-1)+1 = k+1, otherwise a(n) = (A000523(n)+1)*a(A035327(n-1)).

%I A096115 #11 Jul 06 2025 21:38:21
%S A096115 1,2,2,3,6,6,3,4,12,24,24,12,8,8,4,5,20,40,40,60,120,120,60,20,15,30,
%T A096115 30,15,10,10,5,6,30,60,60,90,180,180,90,120,360,720,720,360,240,240,
%U A096115 120,30,24,48,48,72,144,144,72,24,18,36,36,18,12,12,6,7,42,84,84,126
%N A096115 If n = (2^k)-1, a(n) = a((n+1)/2) = k, if n = 2^k, a(n) = a(n-1)+1 = k+1, otherwise a(n) = (A000523(n)+1)*a(A035327(n-1)).
%C A096115 A fractal sequence. For k in range [1,(2^n)-1], a(2^n + k)/a(2^n - k) = n+1. Each n > 1 occurs 2*A045778(n) times in the sequence.
%o A096115 (Scheme) (define (A096115 n) (cond ((pow2? (+ n 1)) (+ 1 (A000523 n))) ((pow2? n) (+ 1 (A096115 (- n 1)))) (else (* (+ (A000523 n) 1) (A096115 (A035327 (- n 1)))))))
%o A096115 (define (pow2? n) (and (> n 0) (zero? (A004198bi n (- n 1)))))
%Y A096115 Permutation of A096111, i.e. a(n) = A096111(A122199(n)-1) [Note the different starting offsets]. Cf. A096113, A052330, A096114, A096116.
%K A096115 nonn
%O A096115 1,2
%A A096115 _Amarnath Murthy_, Jun 30 2004
%E A096115 Edited, extended and Scheme code added by _Antti Karttunen_, Aug 25 2006