A163558 Composite numbers such that exactly six distinct permutations of digits give primes.

1036, 1096, 1099, 1136, 1235, 1238, 1253, 1267, 1276, 1294, 1306, 1316, 1325, 1328, 1352, 1358, 1360, 1378, 1382, 1385, 1387, 1492, 1532, 1538, 1603, 1630, 1631, 1672, 1678, 1687, 1690, 1726, 1738, 1762, 1768, 1786, 1832, 1835, 1837, 1853, 1876, 1906

Offset

1,1

Links

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

Example

a(1) = 1036 because 1036 is composite, the six permutations 163, 613, 631, 1063, 3061, and 6301 are all prime, and no other permutation of 1036 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 >= 7 then return false fi;
    fi
  od;
  evalb(c=6)
end proc:
select(filter, [$10..2000]); # Robert Israel, Dec 30 2025

Mathematica

Select[Range[2000], CompositeQ[#]&&Count[FromDigits/@Permutations[ IntegerDigits[ #]], _?PrimeQ]==6&] (* Harvey P. Dale, Mar 05 2023 *)

Crossrefs

Sequence in context: A023087 A219445 A373407 * A025412 A025409 A043388

Adjacent sequences: A163555 A163556 A163557 * A163559 A163560 A163561

Keyword

easy,nonn,base

Author

Gil Broussard, Jul 30 2009

Status

approved