A364142 Sophie Germain primes p such that both p and the corresponding safe prime 2*p+1 have distinct digits.

2, 3, 23, 29, 41, 53, 83, 89, 173, 179, 239, 251, 281, 293, 359, 419, 431, 491, 641, 653, 683, 719, 743, 761, 953, 1289, 1409, 1439, 1583, 1973, 2039, 2063, 2069, 2351, 2543, 2693, 2741, 2819, 2903, 2963, 3491, 3761, 3821, 4019, 4073, 4271, 4793, 4871, 5231, 6173, 6329, 6491, 6983, 7043, 7103

Offset: 1

Author

Zak Seidov and Robert Israel, Jul 10 2023

Keywords

• nonn
• base
• fini
• full

Comments

Members p of A005384 such that both p and 2*p+1 are in A010784.

The last term is a(1514) = 493250861 and the corresponding safe prime is 2*493250861 + 1 = 986501723.

The b-file contains all 1514 terms.

Examples

			a(4) = 29 is a term because 29 and 2*29 + 1 = 59 are both primes and both have distinct digits.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1514

Crossrefs

Cf. A005384, A005385, A010784.

Programs

Maple

filter:= proc(p) local L;
  L:= convert(p,base,10);
  if nops(L) <> nops(convert(L,set)) or not isprime(2*p+1) then return false fi;
  L:= convert(2*p+1,base,10);
  nops(L) = nops(convert(L,set))
end proc:
select(filter, [seq(ithprime(i),i=1..1000)]);

Mathematica

s = {p = 2}; Do[p = NextPrime[p]; While[! PrimeQ[q = 2*p + 1] || 1<
Max[DigitCount[q]] || 1 < Max[DigitCount[p]], p = NextPrime[p]]; AppendTo[s,
p], {1515}]; s