A285107 a(n) = A001222(A284577(n)).

1, 2, 1, 3, 4, 5, 1, 4, 5, 7, 6, 5, 7, 8, 1, 5, 6, 7, 5, 8, 9, 7, 4, 7, 7, 8, 7, 7, 10, 11, 1, 6, 7, 7, 8, 7, 13, 14, 11, 13, 14, 7, 9, 16, 11, 13, 4, 9, 9, 6, 11, 11, 12, 13, 11, 12, 9, 9, 8, 9, 13, 14, 1, 7, 8, 7, 11, 10, 11, 15, 20, 17, 17, 14, 19, 25, 20, 13, 17, 16, 17, 13, 20, 19, 21, 26, 9, 21, 18, 11, 21, 26, 17, 19, 4, 11, 11, 6, 17, 17, 18, 15, 9

Offset: 0

Author

Antti Karttunen, Apr 11 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A001222, A003987, A007306, A284577, A285106, A285108.

Programs

Scheme

(define (A285107 n) (A001222 (A284577 n)))
;; A more practical version, needing only an implementation of A003987bi (bitwise-xor, A003987) and memoization-macro definec:
(define (bitwise_xor_of_exp_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (bitwise_xor_of_exp_lists nums2 nums1)) (else (map A003987bi 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)))))))

Formula

a(n) = A001222(A284577(n)).

a(n) = A285106(n) - A285108(n).

Other identities. For all n >= 0:

A007306(1+n) = a(n) + 2*A285108(n).