A072733 Simple triangle-stretching N X N -> N bijection: Inverse of A072732.

0, 1, 5, 6, 2, 14, 15, 3, 9, 27, 28, 10, 4, 20, 44, 45, 21, 7, 13, 35, 65, 66, 36, 16, 8, 26, 54, 90, 91, 55, 29, 11, 19, 43, 77, 119, 120, 78, 46, 22, 12, 34, 64, 104, 152, 153, 105, 67, 37, 17, 25, 53, 89, 135, 189, 190, 136, 92, 56, 30, 18, 42, 76, 118, 170, 230, 231

Offset: 0

Author

Antti Karttunen, Jun 12 2002

Keywords

• nonn
• tabl

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A072732, projections: A072738 & A072739, variant of the same theme: A072735. Cf. also A001477 and its projections A025581 & A002262.

Programs

Scheme

(define (A072733 n) (packA072733 (A025581 n) (A002262 n)))
(define (packA001477 x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))
(define (packA072733 x y) (cond ((<= x y) (let ((half-x (floor->exact (/ x 2)))) (packA001477 half-x (+ half-x (* 2 (- y (* 2 half-x) (modulo x 2))) (modulo x 2))))) (else (let ((half-y (floor->exact (/ y 2)))) (packA001477 (+ 1 half-y (* 2 (- (-1+ x) (* 2 half-y) (modulo y 2))) (modulo y 2)) half-y)))))