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A249725 Inverse permutation to A135764. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A230598 A245446 A070264 * A253552 A265896 A254054

Adjacent sequences:  A249722 A249723 A249724 * A249726 A249727 A249728

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 15 2014

STATUS

approved

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Last modified October 23 14:09 EDT 2021. Contains 348214 sequences. (Running on oeis4.)