A249725 Inverse permutation to A135764.

1, 3, 2, 6, 4, 5, 7, 10, 11, 8, 16, 9, 22, 12, 29, 15, 37, 17, 46, 13, 56, 23, 67, 14, 79, 30, 92, 18, 106, 38, 121, 21, 137, 47, 154, 24, 172, 57, 191, 19, 211, 68, 232, 31, 254, 80, 277, 20, 301, 93, 326, 39, 352, 107, 379, 25, 407, 122, 436, 48, 466, 138, 497, 28, 529, 155, 562, 58, 596, 173, 631, 32, 667, 192, 704, 69, 742, 212, 781, 26, 821, 233, 862, 81

Offset: 1

Author

Antti Karttunen, Nov 15 2014

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: A135764.

Similar or related permutations: A209268, A246276, A246676, A249742, A249811.

Cf. A000079, A000124, A000217, A003602, A005408, A007814.

Programs

PARI

a(n) = {r = 1; while(!(n%2), n = n >> 1; r++); k = 1 + n \ 2; binomial(r + k - 1, 2) + r} \\ David A. Corneth, Feb 05 2015

Scheme

(define (A249725 n) (+ 1 (* (/ 1 2) (+ (expt (+ (A003602 n) (A007814 n)) 2) (- (A003602 n)) (A007814 n)))))

Formula

a(n) = 1 + (((A003602(n)+A007814(n))^2 + A007814(n) - A003602(n))/2).

As a composition of other permutations:

a(n) = A249742(A249811(n)).

a(n) = A246276(A246676(n)).

Other identities. For all n >= 0 the following holds:

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

a(A000079(n)) = A000217(n+1). [Maps powers of two to triangular numbers].