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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for sequences that are permutations of the natural numbers

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.]

Prog

(Scheme) (define (A250252 n) (let ((x (A078898 (+ 1 n))) (y (A055396 (+ 1 n)))) (* (/ 1 2) (- (expt (+ x y) 2) x y y y -2))))

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.

Sequence in context: A002475 A208281 A306074 * A246274 A057519 A337659

Adjacent sequences: A250249 A250250 A250251 * A250253 A250254 A250255

Keyword

nonn

Author

Antti Karttunen, Nov 15 2014

Status

approved