A268829 Square array A(row,col) = B(row,(2*col)-1), where B(p,q) = 0 if gcd(p,q) > 1, and 1 + 2*F(p,q) otherwise, where F is defined as in A269158. Array is read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

1, 1, 3, 1, 5, 3, 1, 15, 0, 1, 1, 9, 7, 1, 3, 1, 27, 7, 1, 5, 1, 1, 29, 0, 1, 0, 0, 3, 1, 23, 3, 1, 5, 9, 1, 3, 1, 17, 3, 1, 3, 15, 15, 5, 3, 1, 51, 0, 1, 3, 0, 0, 15, 0, 1, 1, 53, 7, 1, 13, 31, 11, 9, 1, 1, 3, 1, 63, 7, 1, 0, 21, 7, 27, 9, 0, 5, 3, 1, 57, 0, 1, 13, 0, 5, 29, 0, 13, 1, 0, 3, 1, 43, 3, 1, 3, 53, 15, 23, 9, 25, 1, 7, 1, 1

Offset

1,3

Links

Table of n, a(n) for n=1..105.

Formula

A(i,j) = B(i,(2*j)-1), where B(p,q) = 0 if gcd(p,q) > 1, and 1 + 2*F(p,q) = 1 + 2*A269158(p,(q+1)/2) otherwise, where function F is defined as in A269158.

Example

The top left [1 .. 16] x [1 .. 25] section of the array:
1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1
3,  5, 15,  9, 27, 29, 23, 17, 51, 53, 63, 57, 43, 45, 39, 33
3,  0,  7,  7,  0,  3,  3,  0,  7,  7,  0,  3,  3,  0,  7,  7
1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1
3,  5,  0,  5,  3,  3, 13,  0, 13,  3, 11, 13,  0, 13, 11, 11
1,  0,  9, 15,  0, 31, 21,  0, 53, 51,  0, 59, 41,  0, 33, 39
3,  1, 15,  0, 11,  7,  5, 15,  5,  3,  0,  7,  3,  9, 11,  9
3,  5, 15,  9, 27, 29, 23, 17, 51, 53, 63, 57, 43, 45, 39, 33
3,  0,  1,  9,  0,  9, 19,  0, 25,  3,  0,  1, 25,  0,  9, 19
1,  1,  0, 13, 25, 31, 27,  0, 63, 55, 53, 53,  0, 33, 45, 43
3,  5,  1,  1, 27,  0, 15, 23, 29, 27, 29,  7, 17, 21, 21, 31
3,  0,  7,  7,  0,  3,  3,  0,  7,  7,  0,  3,  3,  0,  7,  7
3,  1,  7, 15,  1, 29,  0, 13,  3, 23, 29, 17, 17, 19, 25, 23
1,  5,  1,  0, 17, 27, 19, 31, 55, 55,  0, 63, 41, 37, 45, 41
3,  0,  0,  1,  0,  1, 23,  0, 19,  7,  0, 31,  0,  0,  5, 31
1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1
3,  5, 15,  7, 27, 31,  1, 17,  0, 17, 35, 23, 17, 29, 37, 21
1,  0, 15,  1,  0, 21,  5,  0, 43, 55,  0, 57, 51,  0, 47, 51
3,  1,  1,  5,  1, 29, 21,  1, 51,  0, 23, 39, 17, 19, 21, 33
3,  5,  0,  5,  3,  3, 13,  0, 13,  3, 11, 13,  0, 13, 11, 11
3,  0,  1,  0,  0, 31, 23,  0,  1, 53,  0, 21, 35,  0, 21, 31
1,  1, 15,  9,  1,  0, 25,  7, 47, 47, 35, 63, 59, 57, 51, 63
3,  5,  7,  9,  3,  1, 27, 17, 53,  1, 63,  0, 27, 39, 17, 23
1,  0,  9, 15,  0, 31, 21,  0, 53, 51,  0, 59, 41,  0, 33, 39
3,  1,  0,  1, 11,  3,  3,  0, 51, 51,  1, 57,  0, 25, 51, 27

Prog

(Scheme)
(define (A268829 n) (let ((p (A002260 n)) (q (+ -1 (* 2 (A004736 n))))) (if (< 1 (gcd p q)) 0 (+ 1 (* 2 (A269158auxbi p q)))))) ;; This one uses the code of A269158.
;; The following is a more stand-alone implementation:
(define (A268829 n) (A268829auxbi (A002260 n) (+ -1 (* 2 (A004736 n)))))
(define (A268829auxbi p q) (if (not (odd? q)) (error "A268829auxbi: the second argument should be odd: " p q) (let loop ((p p) (q q) (s 0)) (cond ((zero? p) 0) ((= 1 p) (+ 1 (* 2 s))) ((odd? p) (loop (modulo q p) p (A003987bi s (A004198bi p q)))) (else (loop (/ p 2) q (A003987bi s (A003987bi q (/ (- q 1) 2)))))))))

Crossrefs

Cf. arrays A268728, A269158.

Sequence in context: A206283 A135224 A209578 * A249100 A356255 A152203

Adjacent sequences: A268826 A268827 A268828 * A268830 A268831 A268832

Keyword

nonn,tabl

Author

Antti Karttunen, Feb 20 2016

Status

approved