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A128717 Primes that yield another prime if one adds either the sum of its digits or the product of its digits. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A126118

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

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Last modified September 24 17:09 EDT 2020. Contains 337321 sequences. (Running on oeis4.)