A285108 a(n) = A001222(A284578(n)).

0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 3, 0, 0, 1, 3, 1, 1, 3, 4, 1, 1, 2, 3, 2, 0, 0, 4, 0, 0, 2, 3, 3, 1, 2, 3, 0, 0, 6, 6, 1, 3, 3, 6, 1, 1, 5, 4, 3, 3, 4, 4, 1, 2, 4, 5, 3, 0, 0, 5, 0, 0, 3, 3, 3, 4, 4, 1, 0, 1, 6, 5, 0, 2, 7, 3, 0, 0, 6, 5, 4, 4, 4, 11, 1, 2, 9, 5, 0, 3, 3, 8, 1, 1, 7, 4, 3, 4, 8, 10, 3, 3, 11, 6, 3, 4, 9, 4, 1, 1, 5, 5, 3, 3, 5, 4, 1

Offset

0,7

Links

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

Formula

a(n) = A001222(A284578(n)).

a(n) = A285106(n) - A285107(n).

Other identities. For all n >= 0:

A007306(1+n) = A285106(n) + a(n) = A285107(n) + 2*a(n).

Prog

(Scheme)
(define (A285108 n) (A001222 (A284578 n)))
;; A more practical version, needing only an implementation of A004198bi (bitwise-and, A004198) and memoization-macro definec:
(define (A285108 n) (apply + (bitwise_and_of_exp_lists (A260443as_coeff_list n) (A260443as_coeff_list (+ 1 n)))))
(define (bitwise_and_of_exp_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (bitwise_and_of_exp_lists nums2 nums1)) (else (map A004198bi nums1 (append nums2 (make-list (- len1 len2) 0)))))))
(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)))))))

Crossrefs

Cf. A001222, A004198, A007306, A284578, A285106, A285107.

Sequence in context: A347249 A025438 A220400 * A030216 A357352 A339376

Adjacent sequences: A285105 A285106 A285107 * A285109 A285110 A285111

Keyword

nonn

Author

Antti Karttunen, Apr 11 2017

Status

approved