A046810 Number of anagrams of n that are primes.

0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 1, 0, 1, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 1, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 2, 1, 0, 0, 1, 0, 1, 1, 0, 1, 2, 0

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• easy
• base
• nice

Comments

An anagram of a k-digit number is one of the k! permutations of the digits that does not begin with 0.

Examples

			107 has 2 prime anagrams: 107 and 701 (but not 017 or 071); so a(107) = 2.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A039999, A055098.

Programs

Haskell

import Data.List (permutations, nub)
a046810 n = length $ filter ((== 1) . a010051)
                   $ map read (nub $ filter ((> '0') . head)
                                            $ permutations $ show n)
-- Reinhard Zumkeller, Aug 14 2011

Mathematica

Table[Count[FromDigits/@Select[Permutations[IntegerDigits[n]], First[#] != 0&],?(PrimeQ[#]&)],{n,110}] (* _Harvey P. Dale, Aug 24 2011 *)

Python

from sympy import isprime
from itertools import permutations
def a(n): return len(set(t for p in permutations(str(n)) if p[0]!="0" and isprime(t:=int("".join(p)))))
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Feb 17 2024