A053653 Number of ways to rearrange digits of prime(n)*prime(n+1) to form a prime.

0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 3, 4, 8, 0, 6, 11, 3, 0, 3, 6, 1, 1, 4, 3, 0, 2, 5, 6, 15, 15, 17, 16, 12, 12, 4, 10, 8, 5, 8, 18, 11, 23, 5, 13, 9, 10, 8, 6, 27, 9, 4, 6, 14, 4, 24, 3, 14, 6, 4, 33, 7, 14, 11, 12, 6, 86, 26, 53, 13, 79, 27, 51, 81, 61, 26, 39, 25, 54, 17, 25

Offset: 1

Author

Enoch Haga, Feb 18 2000

Keywords

• easy
• nonn
• look
• base

Comments

Leading zeros are not allowed in the rearranged number.

Examples

			a(8) = 2 because 19*23 = 437 and 2 primes, 347 and 743, can be formed from the digits of 437.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A053652, A053736.

Programs

Mathematica

nfp[n_]:=With[{id=IntegerDigits[n]},Length[Select[FromDigits/@Permutations[id],IntegerLength[ #] ==IntegerLength[n]&&PrimeQ[#]&]]]; nfp/@Times@@@Partition[Prime[Range[90]],2,1] (* Harvey P. Dale, Aug 29 2024 *)

Python

from sympy import isprime, prime
from sympy.utilities.iterables import multiset_permutations as mp
def c(s):
    return sum(1 for t in mp(s) if t[0]!='0' and isprime(int("".join(t))))
def a(n): return c(str(prime(n)*prime(n+1)))
print([a(n) for n in range(1, 72)]) # Michael S. Branicky, Dec 22 2021

Extensions

Edited by Jens Kruse Andersen, Dec 01 2006