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 A277327 Number of distinct primes dividing gcd(A260443(n), A260443(n+1)): a(n) = A001221(A277198(n)). 5

%I #12 Oct 26 2016 15:18:40

%S 0,0,1,0,0,1,2,0,0,2,2,1,1,2,3,0,0,3,2,1,1,2,3,1,1,3,3,2,2,3,4,0,0,4,

%T 3,2,2,3,3,1,1,3,3,2,2,3,4,1,1,4,3,2,2,3,4,2,2,4,4,3,3,4,5,0,0,5,4,3,

%U 3,4,4,2,2,4,3,2,2,3,4,1,1,4,3,2,2,3,4,2,2,4,4,3,3,4,5,1,1,5,4,3,3,4,4,2,2,4,4,3,3,4,5,2,2,5,4,3,3,4,5,3,3

%N Number of distinct primes dividing gcd(A260443(n), A260443(n+1)): a(n) = A001221(A277198(n)).

%C a(n) = number of column positions where both row n and n+1 of A125184 have nonzero number present (when scanned from left), in other words, the number of k such that the term t^k has a nonzero coefficient in both Stern polynomials, B(n,t) and B(n+1,t).

%H Antti Karttunen, <a href="/A277327/b277327.txt">Table of n, a(n) for n = 0..8192</a>

%F a(n) = A001221(A277198(n)).

%F a(n) <= A277328(n).

%o (Scheme)

%o (define (A277327 n) (A001221 (A277198 n)))

%o ;; A standalone implementation:

%o (define (A277327 n) (length (filter positive? (gcd_of_exp_lists (A260443as_coeff_list n) (A260443as_coeff_list (+ 1 n))))))

%o (definec (A260443as_coeff_list n) (cond ((zero? n) (list)) ((= 1 n) (list 1)) ((even? n) (cons 0 (A260443as_coeff_list (/ n 2)))) (else (add_two_lists (A260443as_coeff_list (/ (- n 1) 2)) (A260443as_coeff_list (/ (+ n 1) 2))))))

%o (define (add_two_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (add_two_lists nums2 nums1)) (else (map + nums1 (append nums2 (make-list (- len1 len2) 0)))))))

%o (define (gcd_of_exp_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (gcd_of_exp_lists nums2 nums1)) (else (map min nums1 (append nums2 (make-list (- len1 len2) 0)))))))

%Y Cf. A001221, A125184, A260443, A277198, A277328.

%K nonn

%O 0,7

%A _Antti Karttunen_, Oct 13 2016

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