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

1,1

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.

Links

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

Example

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

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

Crossrefs

Cf. A005384, A005385, A010784.

Sequence in context: A143279 A272271 A068887 * A260128 A220569 A328940

Adjacent sequences: A364139 A364140 A364141 * A364143 A364144 A364145

Keyword

nonn,base,fini,full

Author

Zak Seidov and Robert Israel, Jul 10 2023

Status

approved