A255408 Permutation of natural numbers: a(n) = A083221(A255128(n)).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 25, 20, 21, 22, 19, 24, 23, 26, 27, 28, 29, 30, 49, 32, 33, 34, 35, 36, 31, 38, 39, 40, 37, 42, 41, 44, 45, 46, 43, 48, 55, 50, 51, 52, 47, 54, 121, 56, 57, 58, 77, 60, 53, 62, 63, 64, 65, 66, 59, 68, 69, 70, 61, 72, 169, 74, 75, 76, 67, 78, 85, 80, 81, 82, 71, 84, 91, 86, 87

Offset

1,2

Comments

a(n) tells which number in array A083221 (the sieve of Eratosthenes) is at the same position where n is in Ludic array A255127. 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 A083140 is at the same position where n is in the array A255129, 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) = A083221(A255128(n)).

Other identities. For all n >= 1:

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

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

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

Example

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

Prog

(Scheme) (define (A255408 n) (A083221 (A255128 n)))

Crossrefs

Inverse: A255407.

Cf. A003309, A008578, A083221, A255127, A255128.

Similar permutations: A249817.

Sequence in context: A269395 A302025 A269396 * A269172 A302026 A358373

Adjacent sequences: A255405 A255406 A255407 * A255409 A255410 A255411

Keyword

nonn

Author

Antti Karttunen, Feb 22 2015

Status

approved