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

1,13

Comments

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

Links

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

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A039999, A055098.

Sequence in context: A178665 A170958 A178651 * A328515 A356682 A323989

Adjacent sequences: A046807 A046808 A046809 * A046811 A046812 A046813

Keyword

nonn,easy,base,nice

Author

David W. Wilson

Status

approved