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

163, 233, 293, 431, 499, 563, 617, 743, 1423, 1483, 1489, 1867, 2273, 2543, 2633, 3449, 4211, 4217, 4273, 4547, 4729, 5861, 6121, 6529, 6637, 6653, 6761, 6857, 6949, 7681, 8273, 8431, 8837, 8839, 9649, 9689

Offset: 1

Author

Ray G. Opao, Apr 08 2004

Keywords

• nonn
• base

Comments

Intersection of A048519 and A092518.

Zeros are not permitted in p; thus, for example, 101 is not included. - Harvey P. Dale, May 25 2013

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A048519, A092518.

Programs

Maple

filter:= proc(p) local L;
  if not isprime(p) then return false fi;
  L:= convert(p,base,10);
  if member(0,L) then return false fi;
  isprime(p + convert(L,`+`)) and isprime(p + convert(L,`*`))
end proc:
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Feb 20 2024

Mathematica

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 *)

Extensions

More terms from Robert G. Wilson v, Apr 10 2004