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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), ...
6
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
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
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Feb 20 2016
STATUS
approved