A249811 Permutation of natural numbers: a(n) = A249741(A001511(n), A003602(n)).

1, 2, 3, 4, 5, 8, 7, 6, 9, 14, 11, 24, 13, 20, 15, 10, 17, 26, 19, 34, 21, 32, 23, 48, 25, 38, 27, 54, 29, 44, 31, 12, 33, 50, 35, 64, 37, 56, 39, 76, 41, 62, 43, 84, 45, 68, 47, 120, 49, 74, 51, 94, 53, 80, 55, 90, 57, 86, 59, 114, 61, 92, 63, 16, 65, 98, 67, 124, 69, 104, 71, 118, 73, 110, 75, 144, 77, 116, 79, 142, 81

Offset: 1

Author

Antti Karttunen, Nov 06 2014

Keywords

• nonn

Comments

In the essence, a(n) tells which number in square array A249741 (the sieve of Eratosthenes minus 1) is at the same position where n is in array A135764, which is formed from odd numbers whose binary expansions are shifted successively leftwards on the successive rows. As the topmost row in both arrays is A005408 (odd numbers), they are fixed, i.e., a(2n+1) = 2n+1 for all n.

Equally: a(n) tells which number in array A114881 is at the same position where n is in the array A054582, as they are the transposes of above two arrays.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8191
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A249812.

Cf. A000079, A000265, A001511, A003602, A005408, A006093, A007814, A054582, A083140, A083221, A249741.

Similar or related permutations: A249814 ("deep variant"), A246676, A249815, A114881, A209268, A249725, A249741.

Differs from A246676 for the first time at n=14, where a(14)=20, while

A246676(14)=26.

Programs

Scheme

(define (A249811 n) (+ -1 (A083221bi (A001511 n) (A003602 n))))
;; Code for A083221bi given in A083221

Formula

In the following formulas, A083221 and A249741 are interpreted as bivariate functions:

a(n) = A083221(A001511(n),A003602(n)) - 1 = A249741(A001511(n),A003602(n)).

As a composition of related permutations:

a(n) = A114881(A209268(n)).

a(n) = A249741(A249725(n)).

a(n) = A249815(A246676(n)).

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

a(A000079(n-1)) = A006093(n).