A255407 Permutation of natural numbers: a(n) = A255127(A252460(n)).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 23, 20, 21, 22, 25, 24, 19, 26, 27, 28, 29, 30, 37, 32, 33, 34, 35, 36, 41, 38, 39, 40, 43, 42, 47, 44, 45, 46, 53, 48, 31, 50, 51, 52, 61, 54, 49, 56, 57, 58, 67, 60, 71, 62, 63, 64, 65, 66, 77, 68, 69, 70, 83, 72, 89, 74, 75, 76, 59, 78, 91, 80, 81

Offset

1,2

Comments

a(n) tells which number in Ludic array A255127 is at the same position where n is in array A083221, the sieve of Eratosthenes. As both arrays have A005843 (even numbers) and A016945 as their two topmost rows, both sequences are among the fixed points of this permutation.

Equally: a(n) tells which number in array A255129 is at the same position where n is in the array A083140, as they are the transposes of above two arrays.

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = A255127(A252460(n)).

Other identities. For all n >= 1:

a(2n) = 2n. [Fixes even numbers.]

a(3n) = 3n. [Fixes multiples of three.]

a(A008578(n)) = A003309(n). [Maps noncomposites to Ludic numbers.]

a(A001248(n)) = A254100(n). [Maps squares of primes to "postludic numbers".]

a(A084967(n)) = a(5*A007310(n)) = A007310((5*n)-3) = A255413(n). [Maps A084967 to A255413.]

(And similarly between other columns and rows of A083221 and A255127.)

Example

A083221(8,1) = 19 and A255127(8,1) = 23, thus a(19) = 23.
A083221(9,1) = 23 and A255127(9,1) = 25, thus a(23) = 25.
A083221(3,2) = 25 and A255127(3,2) = 19, thus a(25) = 19.

Prog

(define (A255407 n) (A255127 (A252460 n)))

Crossrefs

Cf. A001248, A003309, A007310, A008578, A083221, A084967, A252460, A254100, A255413, A255127.

Inverse: A255408.

Similar permutations: A249818.

Sequence in context: A246093 A261924 A255421 * A269171 A269395 A302025

Adjacent sequences: A255404 A255405 A255406 * A255408 A255409 A255410

Keyword

nonn

Author

Antti Karttunen, Feb 22 2015

Status

approved