_Antti Karttunen _, Jun 12 2002

<a href="/Sindx_index/Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

<a href="/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

nonn,tabl,new

<a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

nonn,tabl,new

Simple triangle-stretching N X N -> N bijection: Inverse of A072734, variant of A072733.

0, 1, 2, 3, 5, 9, 10, 6, 14, 20, 21, 15, 4, 27, 35, 36, 28, 7, 8, 44, 54, 55, 45, 11, 13, 19, 65, 77, 78, 66, 22, 16, 26, 34, 90, 104, 105, 91, 37, 29, 12, 43, 53, 119, 135, 136, 120, 56, 46, 17, 18, 64, 76, 152, 170, 171, 153, 79, 67, 23, 25, 33, 89, 103, 189, 209, 210

0,3

<a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

(Scheme) (define (A072735 n) (packA072735 (A025581 n) (A002262 n)))

(define (packA001477 x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))

(define (packA072735 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) (if (and (eq? x y) (even? x)) 0 -1))))) (else (let ((half-y (floor->exact (/ y 2)))) (packA001477 (+ half-y (* 2 (- (-1+ x) (* 2 half-y))) (modulo y 2) (if (and (eq? x (1+ y)) (even? y)) 1 0)) half-y)))))

Inverse: A072734, projections: A072781 & A072782, variant of the same theme: A072733. Cf. also A001477 and its projections A025581 & A002262.

nonn,tabl

Antti Karttunen Jun 12 2002

approved