A249812 - OEIS

A249812

Permutation of natural numbers: a(n) = A000079(A055396(n+1)-1) * ((2*A078898(n+1))-1).

1, 2, 3, 4, 5, 8, 7, 6, 9, 16, 11, 32, 13, 10, 15, 64, 17, 128, 19, 14, 21, 256, 23, 12, 25, 18, 27, 512, 29, 1024, 31, 22, 33, 20, 35, 2048, 37, 26, 39, 4096, 41, 8192, 43, 30, 45, 16384, 47, 24, 49, 34, 51, 32768, 53, 28, 55, 38, 57, 65536, 59, 131072, 61, 42, 63, 36, 65, 262144, 67, 46, 69, 524288, 71, 1048576, 73, 50, 75, 40, 77, 2097152, 79, 54, 81, 4194304, 83, 44

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

In the essence, a(n) tells which number in the array A135764 is at the same position where n is in the array A249741, the sieve of Eratosthenes minus 1. 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 A054582 is at the same position where n is in the array A114881, as they are the transposes of above two arrays.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..1024

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = A000079(A055396(n+1)-1) * ((2*A078898(n+1))-1).

As a composition of related permutations:

a(n) = A054582(A250252(n)-1).

a(n) = A135764(A249742(n)).

a(n) = A246675(A249816(n)).

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

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

PROG