A249811 - OEIS

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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

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OFFSET

1,2

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

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).