A092529 - OEIS

%I #18 Feb 21 2024 08:26:59

%S 163,233,293,431,499,563,617,743,1423,1483,1489,1867,2273,2543,2633,

%T 3449,4211,4217,4273,4547,4729,5861,6121,6529,6637,6653,6761,6857,

%U 6949,7681,8273,8431,8837,8839,9649,9689

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

%C Intersection of A048519 and A092518.

%C Zeros are not permitted in p; thus, for example, 101 is not included. - _Harvey P. Dale_, May 25 2013

%H Robert Israel, <a href="/A092529/b092529.txt">Table of n, a(n) for n = 1..10000</a>

%e a(2) = 233: 233+(2+3+3) = 233+8 = 241, which is prime. 233+(2*3*3) = 233+18 = 251, which is prime.

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

%p   if not isprime(p) then return false fi;

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

%p   if member(0,L) then return false fi;

%p   isprime(p + convert(L,`+`)) and isprime(p + convert(L,`*`))

%p end proc:

%p select(filter, [seq(i,i=3..10000,2)]); # _Robert Israel_, Feb 20 2024

%t 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 Cf. A048519, A092518.

%K nonn,base

%O 1,1

%A _Ray G. Opao_, Apr 08 2004

%E More terms from _Robert G. Wilson v_, Apr 10 2004