A086150 Number of permutations of decimal digits of n which yield nonprime numbers.

1, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 0, 1, 2, 1, 0, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 0, 1, 1, 1, 1, 2, 0, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 0, 2, 0, 1, 2, 1, 1, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 0, 1, 1, 3, 1, 6, 3, 4, 6

Offset: 1

Author

Labos Elemer, Aug 04 2003

Keywords

• base
• nonn

Comments

From Robert Israel, Aug 13 2017: (Start)

Leading zeros are allowed.

a(n) = 0 for n in A003459. (End)

Examples

			n=117, digit-permutations={117,171,711} are all composites, so a(117)=3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003459, A039999, A047726.

Programs

Maple

f:= proc(L) option remember;
  nops(remove(isprime, map(t -> add(t[i]*10^(i-1),i=1..nops(t)), combinat:-permute(L))))
end proc:
seq(f(sort(convert(n,base,10))),n=1..200); # Robert Israel, Aug 13 2017

Mathematica

nd[x_, y_] := 10*x+y tn[x_] := Fold[nd, 0, x] Table[Count[Table[PrimeQ[tn[Part[Permutations[ IntegerDigits[w]], j]]], {j, 1, Length[Permutations[ IntegerDigits[w]]]}], False], {w, 1, 128}]
Table[Count[FromDigits/@Permutations[IntegerDigits[n]],?(!PrimeQ[#]&)],{n,110}] (* _Harvey P. Dale, Dec 24 2016 *)

Formula

a(n) + A039999(n) = A047726(n). - Robert Israel, Aug 13 2017