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

%I A364142 #11 Aug 02 2023 13:47:29
%S A364142 2,3,23,29,41,53,83,89,173,179,239,251,281,293,359,419,431,491,641,
%T A364142 653,683,719,743,761,953,1289,1409,1439,1583,1973,2039,2063,2069,2351,
%U A364142 2543,2693,2741,2819,2903,2963,3491,3761,3821,4019,4073,4271,4793,4871,5231,6173,6329,6491,6983,7043,7103
%N A364142 Sophie Germain primes p such that both p and the corresponding safe prime 2*p+1 have distinct digits.
%C A364142 Members p of A005384 such that both p and 2*p+1 are in A010784.
%C A364142 The last term is a(1514) = 493250861 and the corresponding safe prime is 2*493250861 + 1 = 986501723.
%C A364142 The b-file contains all 1514 terms.
%H A364142 Robert Israel, <a href="/A364142/b364142.txt">Table of n, a(n) for n = 1..1514</a>
%e A364142 a(4) = 29 is a term because 29 and 2*29 + 1 = 59 are both primes and both have distinct digits.
%p A364142 filter:= proc(p) local L;
%p A364142   L:= convert(p,base,10);
%p A364142   if nops(L) <> nops(convert(L,set)) or not isprime(2*p+1) then return false fi;
%p A364142   L:= convert(2*p+1,base,10);
%p A364142   nops(L) = nops(convert(L,set))
%p A364142 end proc:
%p A364142 select(filter, [seq(ithprime(i),i=1..1000)]);
%t A364142 s = {p = 2}; Do[p = NextPrime[p]; While[! PrimeQ[q = 2*p + 1] || 1<
%t A364142 Max[DigitCount[q]] || 1 < Max[DigitCount[p]], p = NextPrime[p]]; AppendTo[s,
%t A364142 p], {1515}]; s
%Y A364142 Cf. A005384, A005385, A010784.
%K A364142 nonn,base,fini,full
%O A364142 1,1
%A A364142 _Zak Seidov_ and _Robert Israel_, Jul 10 2023