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A092529 Primes p such that both the digit sum of p plus p and the digit product of p plus p are also primes.

%I A092529 #18 Feb 21 2024 08:26:59
%S A092529 163,233,293,431,499,563,617,743,1423,1483,1489,1867,2273,2543,2633,
%T A092529 3449,4211,4217,4273,4547,4729,5861,6121,6529,6637,6653,6761,6857,
%U A092529 6949,7681,8273,8431,8837,8839,9649,9689
%N A092529 Primes p such that both the digit sum of p plus p and the digit product of p plus p are also primes.
%C A092529 Intersection of A048519 and A092518.
%C A092529 Zeros are not permitted in p; thus, for example, 101 is not included. - _Harvey P. Dale_, May 25 2013
%H A092529 Robert Israel, <a href="/A092529/b092529.txt">Table of n, a(n) for n = 1..10000</a>
%e A092529 a(2) = 233: 233+(2+3+3) = 233+8 = 241, which is prime. 233+(2*3*3) = 233+18 = 251, which is prime.
%p A092529 filter:= proc(p) local L;
%p A092529   if not isprime(p) then return false fi;
%p A092529   L:= convert(p,base,10);
%p A092529   if member(0,L) then return false fi;
%p A092529   isprime(p + convert(L,`+`)) and isprime(p + convert(L,`*`))
%p A092529 end proc:
%p A092529 select(filter, [seq(i,i=3..10000,2)]); # _Robert Israel_, Feb 20 2024
%t A092529 pppQ[n_]:=Module[{idn=IntegerDigits[n]},!MemberQ[idn,0]&&And@@PrimeQ[ {n+ Total[idn], n+Times@@idn}]]; Select[Prime[Range[1200]],pppQ] (* _Harvey P. Dale_, May 25 2013 *)
%Y A092529 Cf. A048519, A092518.
%K A092529 nonn,base
%O A092529 1,1
%A A092529 _Ray G. Opao_, Apr 08 2004
%E A092529 More terms from _Robert G. Wilson v_, Apr 10 2004