A163555 Composite numbers such that exactly three distinct permutations of digits give primes.

130, 136, 175, 176, 301, 310, 316, 361, 370, 371, 395, 398, 517, 539, 671, 703, 713, 715, 716, 730, 731, 893, 935, 938, 1004, 1025, 1027, 1034, 1040, 1043, 1052, 1058, 1072, 1085, 1118, 1124, 1142, 1147, 1169, 1174, 1189, 1196, 1198, 1205, 1207, 1214

Offset

1,1

Links

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

Example

a(1) = 130 because 130 is composite and 13, 31, and 103 are prime permutations, and no other permutation of 130 is prime.

Maple

filter:= proc(n) local d, Permutor, P, c, i;
  if isprime(n) then return false fi;
  d:= ilog10(n)+1;
  Permutor:= Iterator:-Permute(convert(n, base, 10));
  c:= 0;
  for P in Permutor do
    if isprime(add(P[i]*10^(i-1), i=1..d)) then
      c:= c+1;
      if c >= 4 then return false fi;
    fi
  od;
  evalb(c=3)
end proc:
select(filter, [$100..2000]); # Robert Israel, Aug 10 2020

Mathematica

With[{no=1400}, Select[Complement[Range[no], Prime[Range[PrimePi[no]]]], Count[FromDigits/@Permutations[IntegerDigits[#]], _?PrimeQ]==3&]]  (* Harvey P. Dale, Feb 25 2011 *)
Select[Range[1250], CompositeQ[#]&&Total[Boole[PrimeQ[FromDigits/@Permutations[IntegerDigits[#]]]]]==3&] (* Harvey P. Dale, Dec 08 2025 *)

Crossrefs

Cf. A163554, A163556, A163557, A163558, A163559, A163560, A163561, A163562.

Sequence in context: A025372 A378313 A045049 * A025373 A025364 A294311

Adjacent sequences: A163552 A163553 A163554 * A163556 A163557 A163558

Keyword

easy,nonn,base

Author

Gil Broussard, Jul 30 2009

Status

approved