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

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, 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, 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

Offset: 0

Author

Antti Karttunen, Oct 13 2016

Keywords

• nonn

Comments

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).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8192

Crossrefs

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

Programs

Scheme

(define (A277327 n) (A001221 (A277198 n)))
;; A standalone implementation:
(define (A277327 n) (length (filter positive? (gcd_of_exp_lists (A260443as_coeff_list n) (A260443as_coeff_list (+ 1 n))))))
(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))))))
(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)))))))
(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)))))))

Formula

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

a(n) <= A277328(n).