A249742 Inverse permutation to A249741.

1, 3, 2, 6, 4, 10, 7, 5, 11, 15, 16, 21, 22, 8, 29, 28, 37, 36, 46, 12, 56, 45, 67, 9, 79, 17, 92, 55, 106, 66, 121, 23, 137, 13, 154, 78, 172, 30, 191, 91, 211, 105, 232, 38, 254, 120, 277, 14, 301, 47, 326, 136, 352, 18, 379, 57, 407, 153, 436, 171, 466, 68, 497, 24, 529, 190, 562, 80, 596, 210, 631, 231, 667, 93, 704, 19

Offset: 1

Author

Antti Karttunen, Nov 15 2014

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A249741.

Cf. A000124, A000217, A005408, A006093, A055396, A078898.

Similar or related permutations: A249725, A249812, A250252.

Differs from A246276 for the first time at n=20, where a(20) = 12, while A246276(20) = 17.

Programs

Scheme

(define (A249742 n) (let ((x (A055396 (+ 1 n))) (y (A078898 (+ 1 n)))) (* (/ 1 2) (- (expt (+ x y) 2) x y y y -2))))

Formula

a(n) = 1 + ((((x+y)^2) - x - 3*y)/2), where x = A055396(n+1) and y = A078898(n+1).

As a composition of related permutations:

a(n) = A249725(A249812(n)).

Other identities.

For all n >= 0 the following holds:

a(A005408(n)) = A000124(n). [Maps odd numbers to central polygonal numbers.]

For all n >= 1 the following holds:

a(A006093(n)) = A000217(n). [Maps precedents of primes to triangular numbers.]