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

1,7

Links

Table of n, a(n) for n=1..49.

Formula

a(n) = A039999(A000079(n)).

Example

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}.

Mathematica

Table[Count[FromDigits/@Permutations[IntegerDigits[2^n]], _?PrimeQ], {n, 50}] (* Harvey P. Dale, Mar 04 2026 *)

Prog

(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
(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

Crossrefs

Cf. A039999, A086150, A000079.

Sequence in context: A206823 A335407 A151668 * A099040 A185296 A136717

Adjacent sequences: A086148 A086149 A086150 * A086152 A086153 A086154

Keyword

base,nonn

Author

Labos Elemer, Aug 04 2003

Extensions

a(27)-a(44) from Andrew Howroyd, Jan 05 2020

a(45)-a(49) from Michael S. Branicky, May 26 2023

Previous Mathematica program replaced by Harvey P. Dale, Mar 04 2026

Status

approved