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

%I A227217 #56 Mar 21 2020 16:37:59
%S A227217 23,29,83,101,103,107,109,293,307,347,349,401,409,431,439,503,509,601,
%T A227217 607,653,659,677,701,709,743,809,907,1009,1013,1019,1021,1031,1033,
%U A227217 1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1123,1201,1297,1301,1303,1307,1409,1423,1489,1523
%N A227217 Primes p such that p + (product of digits of p) is prime and p - (product of digits of p) is prime.
%C A227217 Intersection of A157677 and A225319.
%C A227217 Contains A056709. - _Robert Israel_, Apr 13 2015
%H A227217 Michael De Vlieger, <a href="/A227217/b227217.txt">Table of n, a(n) for n = 1..10000</a>
%e A227217 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.
%p A227217 filter:= proc(n) local m;
%p A227217   if not isprime(n) then return false fi;
%p A227217   m:= convert(convert(n,base,10),`*`);
%p A227217   if m = 0 then return true fi;
%p A227217   isprime(n+m) and isprime(n-m)
%p A227217 end proc:
%p A227217 select(filter, [seq(2*i+1,i=5..10000)]); # _Robert Israel_, Apr 13 2015
%t A227217 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 *)
%o A227217 (Python)
%o A227217 from sympy import isprime, primerange
%o A227217 def DP(n):
%o A227217     p = 1
%o A227217     for i in str(n):
%o A227217         p *= int(i)
%o A227217     return p
%o A227217 for pn in primerange(1, 2000):
%o A227217     dpn = DP(pn)
%o A227217     if isprime(pn-dpn) and isprime(pn+dpn):
%o A227217         print(pn, end=', ')
%o A227217 # Simplified by _Derek Orr_, Apr 10 2015
%o A227217 (Sage)
%o A227217 [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
%o A227217 (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
%Y A227217 Cf. A007954, A056709, A157677, A225319.
%K A227217 nonn,base
%O A227217 1,1
%A A227217 _Derek Orr_, Sep 19 2013
%E A227217 More terms from _Derek Orr_, Apr 10 2015