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A253046
An involution of the natural numbers: if n = 2*p_i then replace n with 3*p_{i+1}, and conversely if n = 3*p_i then replace n with 2*p_{i-1}, where p_i denotes the i-th prime.
7
1, 2, 3, 9, 5, 15, 7, 8, 4, 21, 11, 12, 13, 33, 6, 16, 17, 18, 19, 20, 10, 39, 23, 24, 25, 51, 27, 28, 29, 30, 31, 32, 14, 57, 35, 36, 37, 69, 22, 40, 41, 42, 43, 44, 45, 87, 47, 48, 49, 50, 26, 52, 53, 54, 55, 56, 34, 93, 59, 60, 61, 111, 63, 64, 65, 66, 67
OFFSET
1,2
COMMENTS
a(m) != m iff m is a term of A253106, i.e., a semiprime divisible by 2 or 3; a(A100484(n)) > A100484(n); a(A001748(n)) < A001748(n). - Reinhard Zumkeller, Dec 26 2014
MATHEMATICA
a253046[n_] := Block[{f},
f[x_] := Which[PrimeQ[x/2], 3 NextPrime[x/2],
PrimeQ[x/3], 2 NextPrime[x/3, -1],
True, x]; Array[f, n]]; a253046[67] (* Michael De Vlieger, Dec 27 2014 *)
PROG
(Haskell)
a253046 n | i == 0 || p > 3 = n
| p == 2 = 3 * a000040 (i + 1)
| otherwise = 2 * a000040 (i - 1)
where i = a049084 (div n p); p = a020639 n
-- Reinhard Zumkeller, Dec 26 2014
(Python)
from sympy import isprime, nextprime, prevprime
def A253046(n):
....q2, r2 = divmod(n, 2)
....if not r2 and isprime(q2):
........return 3*nextprime(q2)
....else:
........q3, r3 = divmod(n, 3)
........if not r3 and isprime(q3):
............return 2*prevprime(q3)
........return n # Chai Wah Wu, Dec 27 2014
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 26 2014
STATUS
approved