A244321 Permutation of natural numbers: a(1)=1; thereafter, if n is k-th number whose greatest prime factor has an odd index [i.e., n = A244991(k)], a(n) = 2*a(k), otherwise, when n is k-th number whose greatest prime factor has an even index [i.e., n = A244990(1+k)], a(n) = 1+(2*a(k)).

1, 2, 3, 4, 6, 5, 7, 8, 9, 12, 10, 13, 11, 15, 14, 16, 18, 17, 19, 24, 25, 20, 26, 21, 22, 27, 23, 31, 29, 30, 28, 32, 36, 34, 33, 37, 35, 39, 49, 38, 48, 51, 41, 50, 40, 52, 42, 53, 43, 44, 54, 45, 55, 47, 46, 63, 59, 61, 62, 58, 57, 60, 65, 56, 73, 64, 72, 68, 66, 69

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10001

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, and for n > 1, if A244992(n) = 1 [i.e. the greatest prime factor of n has an odd index], a(n) = 2 * A244321(A244989(n)), otherwise, a(n) = 1 + (2 * A244321(A244988(n)-1)).

For all n >= 1, A000035(a(n)) = 1 - A244992(n).

Prog

(Scheme, with memoization macro definec)
(definec (A244321 n) (cond ((= 1 n) 1) ((= 1 (A244992 n)) (* 2 (A244321 (A244989 n)))) (else (+ 1 (* 2 (A244321 (-1+ (A244988 n))))))))

Crossrefs

Inverse: A244322.

Cf. A244988, A244989, A244990, A244991, A244992.

Similar entanglement permutations: A135141, A237427, A243287, A243343, A243345.

Sequence in context: A057511 A121730 A275659 * A364824 A062894 A339723

Adjacent sequences: A244318 A244319 A244320 * A244322 A244323 A244324

Keyword

nonn

Author

Antti Karttunen, Jul 22 2014

Status

approved