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

Author

N. J. A. Sloane, Dec 26 2014

Keywords

• nonn

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

Crossrefs

Cf. A064614, A253046.

Cf. A020639, A010051, A001751.

Programs

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

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 *)

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