A086151 Number of permutations of decimal digits of 2^n which yield a prime.
1, 0, 0, 1, 1, 0, 2, 0, 2, 4, 0, 0, 5, 19, 10, 3, 87, 9, 0, 377, 293, 84, 9, 265, 142, 502, 4916, 979, 30453, 38758, 15274, 5270, 10463, 81628, 69189, 91023, 1605954, 378559, 152874, 3447170, 220776, 4350954, 1746163, 51889555, 12949705, 5145813, 202624585, 404342074, 118292490
Offset: 1
Examples
n=19: 2^19 = 524288, has 180 permutations, each composite, a(19)=0;
n=13: 2^13 = 8192, the following 5 of the 24 permutations provide primes: {8219, 8291, 1289, 9281, 2819}.
Programs
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Mathematica
Table[Count[Table[PrimeQ[tn[Part[Permutations[ IntegerDigits[2^w]], j]]], {j, 1, Length[Permutations[ IntegerDigits[2^w]]]}], True], {w, 1, 20}] -
PARI
\\ here b(n) is A039999. b(n)={my(D=vecsort(digits(n)), S=0); forperm(D, p, if(isprime(fromdigits(Vec(p))), S++)); S} { for(n=1, 30, print1(b(2^n), ", ")) } \\ Andrew Howroyd, Jan 05 2020
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Python
from sympy import isprime from sympy.utilities.iterables import multiset_permutations as mp def a(n): return sum(1 for p in mp(str(2**n)) if isprime(int("".join(p)))) print([a(n) for n in range(1, 31)]) # Michael S. Branicky, May 25 2023
Extensions
a(27)-a(44) from Andrew Howroyd, Jan 05 2020
a(45)-a(49) from Michael S. Branicky, May 26 2023