A251561 A permutation of the natural numbers: interchange p and 2p for every prime p.

1, 4, 6, 2, 10, 3, 14, 8, 9, 5, 22, 12, 26, 7, 15, 16, 34, 18, 38, 20, 21, 11, 46, 24, 25, 13, 27, 28, 58, 30, 62, 32, 33, 17, 35, 36, 74, 19, 39, 40, 82, 42, 86, 44, 45, 23, 94, 48, 49, 50, 51, 52, 106, 54, 55, 56, 57, 29, 118, 60, 122, 31, 63, 64, 65, 66

Offset

1,2

Comments

a(A001751(n)) != A001751(n). - Reinhard Zumkeller, Dec 27 2014

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

A. B. Frizell, Certain non-enumerable sets of infinite permutations. Bull. Amer. Math. Soc. 21 (1915), no. 10, 495-499.

Index entries for sequences that are permutations of the natural numbers

Mathematica

a251561[n_] := Block[{f}, f[x_] := Which[PrimeQ[x], 2 x, PrimeQ[x/2], x/2, True, x]; Array[f, n]]; a251561[66] (* Michael De Vlieger, Dec 26 2014 *)

Prog

(Python)
from sympy import isprime
def A251561(n):
....if n == 2:
........return 4
....q, r = divmod(n, 2)
....if r :
........if isprime(n):
............return 2*n
........return n
....if isprime(q):
........return q
....return n # Chai Wah Wu, Dec 26 2014
(Haskell)
a251561 1 = 1
a251561 n | q == 1                    = 2 * p
          | p == 2 && a010051' q == 1 = q
          | otherwise                 = n
          where q = div n p; p = a020639 n
-- Reinhard Zumkeller, Dec 27 2014

Crossrefs

Cf. A064614, A253046.

Cf. A020639, A010051, A001751.

Sequence in context: A095196 A074828 A282028 * A159193 A118967 A366952

Adjacent sequences: A251558 A251559 A251560 * A251562 A251563 A251564

Keyword

nonn

Author

N. J. A. Sloane, Dec 26 2014

Status

approved