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

Offset: 1

Author

Antti Karttunen, Nov 06 2014

Keywords

• nonn

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

Crossrefs

Inverse: A249811.

Cf. A000079, A005408, A006093, A055396, A078898.

Similar or related permutations: A249813 ("deep variant"), A246675, A249816, A054582, A114881, A250252, A135764, A249741, A249742.

Differs from A246675 for the first time at n=20, where a(20)=14, while A246675(20)=18.

Programs

Scheme

(define (A249812 n) (* (A000079 (- (A055396 (+ 1 n)) 1)) (+ -1 (* 2 (A078898 (+ 1 n))))))

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).