A227217 Primes p such that p + (product of digits of p) is prime and p - (product of digits of p) is prime.

23, 29, 83, 101, 103, 107, 109, 293, 307, 347, 349, 401, 409, 431, 439, 503, 509, 601, 607, 653, 659, 677, 701, 709, 743, 809, 907, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1123, 1201, 1297, 1301, 1303, 1307, 1409, 1423, 1489, 1523

Offset

1,1

Comments

Intersection of A157677 and A225319.

Contains A056709. - Robert Israel, Apr 13 2015

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

431 is prime, 431 + (4*3*1) = 443 is prime, and 431 - (4*3*1) = 419 is prime. So, 431 is a term in the sequence.

Maple

filter:= proc(n) local m;
  if not isprime(n) then return false fi;
  m:= convert(convert(n, base, 10), `*`);
  if m = 0 then return true fi;
  isprime(n+m) and isprime(n-m)
end proc:
select(filter, [seq(2*i+1, i=5..10000)]); # Robert Israel, Apr 13 2015

Mathematica

fQ[n_] := Block[{d = IntegerDigits@ n}, PrimeQ[n + Times @@ d] && PrimeQ[n - Times @@ d]]; Select[Prime@ Range@ 250, fQ] (* Michael De Vlieger, Apr 12 2015 *)

Prog

(Python)
from sympy import isprime, primerange
def DP(n):
    p = 1
    for i in str(n):
        p *= int(i)
    return p
for pn in primerange(1, 2000):
    dpn = DP(pn)
    if isprime(pn-dpn) and isprime(pn+dpn):
        print(pn, end=', ')
# Simplified by Derek Orr, Apr 10 2015
(Sage)
[p for p in primes_first_n(1000) if ((p-prod(Integer(p).digits(base=10))) in Primes() and (p+prod(Integer(p).digits(base=10))) in Primes())] # Tom Edgar, Sep 19 2013
(PARI) forprime(p=1, 2000, d=digits(p); P=prod(i=1, #d, d[i]); if(isprime(p+P)&&isprime(p-P), print1(p, ", "))) \\ Derek Orr, Apr 10 2015

Crossrefs

Cf. A007954, A056709, A157677, A225319.

Sequence in context: A110584 A115396 A180538 * A229176 A232726 A029541

Adjacent sequences: A227214 A227215 A227216 * A227218 A227219 A227220

Keyword

nonn,base

Author

Derek Orr, Sep 19 2013

Extensions

More terms from Derek Orr, Apr 10 2015

Status

approved