A163556 Composite numbers such that exactly four distinct permutations of decimal digits are prime.

170, 194, 710, 790, 791, 793, 914, 917, 970, 973, 1003, 1012, 1015, 1016, 1024, 1028, 1030, 1042, 1082, 1090, 1102, 1105, 1106, 1120, 1126, 1135, 1138, 1150, 1157, 1159, 1160, 1162, 1175, 1178, 1183, 1195, 1204, 1208, 1210, 1216, 1234, 1240, 1243, 1258

Offset

1,1

Links

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

Example

a(1) = 170 because 170 is composite, the four permutations 17, 71, 107, and 701 are all prime, and no other permutation of 170 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 >= 5 then return false fi;
    fi
  od;
  evalb(c=4)
end proc:
select(filter, [$10..2000]); # Robert Israel, Aug 10 2020

Mathematica

Select[Range[1300], CompositeQ[#]&&Count[FromDigits/@Permutations[ IntegerDigits[ #]], _?PrimeQ]==4&] (* Harvey P. Dale, Oct 26 2015 *)

Crossrefs

Cf. A163554, A163555, A163557, A163558, A163559, A163560, A163561, A163562.

Sequence in context: A043658 A296892 A045002 * A229467 A218071 A113789

Adjacent sequences: A163553 A163554 A163555 * A163557 A163558 A163559

Keyword

easy,nonn,base

Author

Gil Broussard, Jul 30 2009

Status

approved