A250252 Inverse permutation to A114881.

1, 2, 3, 4, 6, 7, 10, 5, 15, 11, 21, 16, 28, 9, 36, 22, 45, 29, 55, 14, 66, 37, 78, 8, 91, 20, 105, 46, 120, 56, 136, 27, 153, 13, 171, 67, 190, 35, 210, 79, 231, 92, 253, 44, 276, 106, 300, 12, 325, 54, 351, 121, 378, 19, 406, 65, 435, 137, 465, 154, 496, 77, 528, 26, 561, 172, 595, 90, 630, 191, 666, 211, 703, 104, 741, 18

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: A114881.

Similar or related permutations: A209268, A249812.

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

Differs from A246274 for the first time at n=20, where a(20) = 14, while

A246274(20) = 20.

Programs

Scheme

(define (A250252 n) (let ((x (A078898 (+ 1 n))) (y (A055396 (+ 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 = A078898(n+1) and y = A055396(n+1).

As a composition of related permutations:

a(n) = A209268(A249812(n)).

Other identities. For all n >= 1 the following holds:

a(A005408(n-1)) = A000217(n). [Maps odd numbers to triangular numbers.]

a(A006093(n)) = A000124(n-1). [Maps precedents of primes to central polygonal numbers.]