A163559 Composite numbers such that exactly seven distinct permutations of digits give primes.

1037, 1073, 1190, 1247, 1274, 1345, 1354, 1370, 1379, 1397, 1435, 1472, 1495, 1534, 1594, 1679, 1703, 1724, 1730, 1739, 1742, 1769, 1793, 1796, 1910, 1937, 1945, 1954, 1967, 1976, 2093, 2147, 2174, 2374, 2390, 2471, 2597, 2714, 2734, 2743, 2759, 2795

Offset

1,1

Links

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

Example

a(1) = 1037 because 1037 is composite and 137, 173, 317, 1307, 3701, 7013, and 7103 are prime permutations, and no other permutation of 1037 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 >= 8 then return false fi;
    fi
  od;
  evalb(c=7)
end proc:
select(filter, [$10..3000]); # Robert Israel, Dec 31 2025

Mathematica

Select[Range[3000], !PrimeQ[#]&&Count[Union[FromDigits/@ Permutations[ IntegerDigits[ #]]], _?PrimeQ]==7&] (* Harvey P. Dale, Apr 16 2013 *)

Crossrefs

Sequence in context: A025409 A043388 A184210 * A159052 A065572 A251876

Adjacent sequences: A163556 A163557 A163558 * A163560 A163561 A163562

Keyword

easy,nonn,base

Author

Gil Broussard, Jul 30 2009

Extensions

Example moved from Maple field to Example field by Harvey P. Dale, Apr 16 2013

Status

approved