A163557 Composite numbers such that exactly five distinct permutations of digits give primes.

1007, 1018, 1057, 1067, 1070, 1075, 1076, 1081, 1108, 1127, 1172, 1180, 1271, 1298, 1330, 1336, 1337, 1339, 1363, 1369, 1393, 1396, 1468, 1486, 1507, 1570, 1576, 1633, 1639, 1648, 1670, 1675, 1684, 1696, 1700, 1705, 1706, 1712, 1750, 1756, 1760, 1765

Offset

1,1

Links

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

Example

a(1) = 1007 because 1007 is composite, the five permutations 17, 71, 107, 701, and 7001 are all prime, and no other permutation of 1007 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 >= 6 then return false fi;
    fi
  od;
  evalb(c=5)
end proc:
select(filter, [$10..2000]); # Robert Israel, Dec 30 2025

Prog

(PARI) upto(m)= my(r=List()); forcomposite(n=1, m, my(d=vecsort(digits(n)), c=0); forperm(d, p, (c+=isprime(fromdigits(p)))>5 && break); 5==c && listput(r, n)); Vec(r); \\ Ruud H.G. van Tol, Jan 02 2026

Crossrefs

Sequence in context: A202147 A252417 A067918 * A241932 A160451 A254973

Adjacent sequences: A163554 A163555 A163556 * A163558 A163559 A163560

Keyword

easy,nonn,base

Author

Gil Broussard, Jul 30 2009

Extensions

Checked by Zak Seidov, Jul 01 2009

Status

approved