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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

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].

Prog

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

Crossrefs

Inverse: A135764.

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

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

Sequence in context: A245446 A070264 A365233 * A253552 A265896 A254054

Adjacent sequences: A249722 A249723 A249724 * A249726 A249727 A249728

Keyword

nonn

Author

Antti Karttunen, Nov 15 2014

Status

approved