A256998 Inverse to A256997 considered as a permutation of natural numbers, with the assumed fixed term a(1) = 1.

1, 2, 4, 7, 3, 5, 11, 6, 8, 9, 16, 12, 17, 23, 10, 13, 30, 14, 22, 38, 47, 18, 24, 57, 31, 15, 68, 80, 93, 107, 19, 39, 122, 20, 29, 138, 155, 48, 58, 173, 25, 32, 192, 212, 233, 69, 40, 255, 21, 81, 278, 302, 94, 108, 327, 123, 26, 353, 380, 408, 437, 467, 49, 139, 498, 27, 37, 530, 563, 156, 174, 597, 59, 70, 632, 668, 705, 193, 33, 743, 41

Offset: 1

Author

Antti Karttunen, Apr 14 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A256997.

Cf. A256989, A256990.

Cf. also A256996, A255558.

Programs

Scheme

(define (A256998 n) (if (= 1 n) n (let ((row (A256989 n)) (col (A256990 n))) (+ 1 (* (/ 1 2) (- (expt (+ row col) 2) row col col col -2))))))

Formula

a(1) = 1, and for n > 1: a(n) = (1/2) * ((c+r)^2 - r - 3*c + 4), where r = A256989(n), and c = A256990(n).