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

1,10

Comments

From Robert Israel, Aug 13 2017: (Start)

Leading zeros are allowed.

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

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A003459, A039999, A047726.

Sequence in context: A218907 A192575 A029401 * A105166 A321299 A105783

Adjacent sequences: A086147 A086148 A086149 * A086151 A086152 A086153

Keyword

base,nonn

Author

Labos Elemer, Aug 04 2003

Status

approved