A364142 - OEIS

%I #11 Aug 02 2023 13:47:29

%S 2,3,23,29,41,53,83,89,173,179,239,251,281,293,359,419,431,491,641,

%T 653,683,719,743,761,953,1289,1409,1439,1583,1973,2039,2063,2069,2351,

%U 2543,2693,2741,2819,2903,2963,3491,3761,3821,4019,4073,4271,4793,4871,5231,6173,6329,6491,6983,7043,7103

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

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

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

%C The b-file contains all 1514 terms.

%H Robert Israel, <a href="/A364142/b364142.txt">Table of n, a(n) for n = 1..1514</a>

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

%p filter:= proc(p) local L;

%p   L:= convert(p,base,10);

%p   if nops(L) <> nops(convert(L,set)) or not isprime(2*p+1) then return false fi;

%p   L:= convert(2*p+1,base,10);

%p   nops(L) = nops(convert(L,set))

%p end proc:

%p select(filter, [seq(ithprime(i),i=1..1000)]);

%t s = {p = 2}; Do[p = NextPrime[p]; While[! PrimeQ[q = 2*p + 1] || 1<

%t Max[DigitCount[q]] || 1 < Max[DigitCount[p]], p = NextPrime[p]]; AppendTo[s,

%t p], {1515}]; s

%Y Cf. A005384, A005385, A010784.

%K nonn,base,fini,full

%O 1,1

%A _Zak Seidov_ and _Robert Israel_, Jul 10 2023