A128717 Primes that yield another prime if one adds either the sum of its digits or the product of its digits.

101, 103, 163, 233, 293, 307, 431, 499, 509, 563, 617, 701, 743, 1009, 1049, 1061, 1087, 1409, 1423, 1483, 1489, 1601, 1607, 1801, 1867, 2017, 2039, 2053, 2273, 2543, 2633, 2903, 3041, 3067, 3089, 3449, 3607, 4013, 4057, 4079, 4211, 4217, 4273, 4507

Offset

1,1

Links

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

Example

163 + (1+6+3) = 173, 163 + 1*6*3 = 181; 173 and 181 are prime numbers.

Maple

filter:= proc(n) local S;
  S:= convert(n, base, 10);
  isprime(n+convert(S, `+`)) and isprime(n+convert(S, `*`))
end proc:
A:= NULL:
p:= 2:
while p < 10000 do
  if filter(p) then A:= A, p fi;
  p:= nextprime(p)
od:
A; # Robert Israel, Jul 12 2017

Mathematica

Select[Prime[Range[500]], PrimeQ[ # + Plus @@ IntegerDigits[ # ]] && PrimeQ[ # + Times @@ IntegerDigits[ # ]] &]

Prog

(PARI) isok(n) = isprime(n) && (isprime(n+sumdigits(n)) && ((d=digits(n)) && isprime(n+prod(k=1, #d, d[k])))); \\ Michel Marcus, Jul 12 2017

Crossrefs

Cf. A048519.

Sequence in context: A176929 A330563 A060400 * A111348 A081649 A344802

Adjacent sequences: A128714 A128715 A128716 * A128718 A128719 A128720

Keyword

base,easy,nonn

Author

J. M. Bergot, Jun 27 2007

Extensions

Edited, corrected and extended by Stefan Steinerberger, Jul 14 2007

Status

approved