A039999 Number of permutations of digits of n which yield distinct primes.

0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 1, 0, 1, 2, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 1, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 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, 2, 0, 3, 2, 0

Offset

1,13

Comments

Consider all k! permutations of digits of a k-digit number n, discard initial zeros, count distinct primes.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

C. Hilliard, PARI program.

Example

a(20) = 1, since from {02, 20} we get {2,20} and only 2 is prime.
From 107 we get 4 primes: (0)17, (0)71, 107 and 701; so a(107) = 4.

Mathematica

Table[Count[FromDigits/@Permutations[IntegerDigits[n]], _?PrimeQ], {n, 110}] (* Harvey P. Dale, Jun 26 2011 *)

Prog

(PARI) for(x=1, 400, print1(permprime(x), ", ")) /* for definition of function permprime cf. link */ \\ Cino Hilliard, Jun 07 2009
(PARI) A039999(n, D=vecsort(digits(n)), S)={forperm(D, p, isprime(fromdigits(Vec(p))) && S++); S} \\ Giving the 2nd arg avoids computing it and increases efficiency when the digits are already known. Must be sorted because forperm() only considers "larger" permutations. - M. F. Hasler, Oct 14 2019
(Magma) [ #[ s: s in Seqset([ Seqint([m(p[i]):i in [1..#x] ], 10): p in Permutations(Seqset(x)) ]) | IsPrime(s) ] where m is map< x->y | [<x[i], y[i]>:i in [1..#x] ] > where x is [1..#y] where y is Intseq(n, 10): n in [1..120] ]; // Klaus Brockhaus, Jun 15 2009
(Haskell)
import Data.List (permutations, nub)
a039999 n = length $ filter ((== 1) . a010051)
                   (map read (nub $ permutations $ show n) :: [Integer])
-- Reinhard Zumkeller, Feb 07 2011
(Python)
from sympy import isprime
from itertools import permutations
def a(n): return len(set(t for p in permutations(str(n)) if isprime(t:=int("".join(p)))))
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Feb 17 2024

Crossrefs

Cf. A046810.

Cf. A039993 (number of primes embedded in n), A076730 (maximum for n digits), A072857 (record indices: primeval numbers), A134596 (largest with n digits).

Cf. A075053 (as A039993 but counted with multiplicity), A134597 (maximum for n digits).

Sequence in context: A356682 A323989 A262988 * A069842 A083056 A356733

Adjacent sequences: A039996 A039997 A039998 * A040000 A040001 A040002

Keyword

nonn,base,nice

Author

David W. Wilson

Extensions

Contribution of Cino Hilliard edited by Klaus Brockhaus, Jun 15 2009

Edited by M. F. Hasler, Oct 14 2019

Status

approved