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

1,1

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A048519, A092518.

Sequence in context: A132250 A303379 A142940 * A142373 A142534 A142695

Adjacent sequences: A092526 A092527 A092528 * A092530 A092531 A092532

Keyword

nonn,base

Author

Ray G. Opao, Apr 08 2004

Extensions

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

Status

approved