A246363 Permutation of natural numbers: a(n) = A135141(A048673(n)).

1, 2, 4, 8, 3, 9, 5, 13, 10, 16, 6, 14, 7, 12, 35, 20, 17, 79, 11, 67, 71, 33, 19, 271, 39, 31, 139, 87, 15, 30, 18, 311, 47, 34, 63, 74, 23, 29, 26, 351, 21, 28, 27, 24, 303, 69, 25, 2431, 70, 223, 135, 319, 37, 1663, 65, 58, 41, 38, 32, 219, 43, 127, 367, 327, 287, 239, 55, 107, 46, 283, 22, 413, 51, 53, 147

Offset

1,2

Comments

Apart from 2, even numbers occur only in positions given by A246261 (together with some odd numbers).

Also, apart from A246263(1) = 2, the positions given by the rest of A246263: 5, 6, 7, 8, 15, 17, 18, 19, 20, 21, ... contain odd numbers only.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = A135141(A048673(n)).

Prog

(PARI)
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of Michel Marcus
A048673(n) = (A003961(n)+1)/2;
A135141(n) = if(1==n, 1, if(isprime(n), 2*A135141(primepi(n)), 1+(2*A135141(n-primepi(n)-1))));
A246363(n) = A135141(A048673(n));
for(n=1, 10000, write("b246363.txt", n, " ", A246363(n)));
(Scheme) (define (A246363 n) (A135141 (A048673 n)))

Crossrefs

Inverse: A246364.

Related or similar permutations: A048673, A135141, A246365, A246367.

Cf. A000035, A003961, A246260, A246261, A246263.

Sequence in context: A367750 A197382 A332521 * A319268 A277272 A109588

Adjacent sequences: A246360 A246361 A246362 * A246364 A246365 A246366

Keyword

nonn

Author

Antti Karttunen, Aug 26 2014

Status

approved