A229176 Primes p with nonzero digits such that p + product_of_digits and p - product_of_digits are both prime.
23, 29, 83, 293, 347, 349, 431, 439, 653, 659, 677, 743, 1123, 1297, 1423, 1489, 1523, 1657, 1867, 2239, 2377, 2459, 2467, 2543, 2579, 2663, 2753, 3163, 3253, 3271, 3329, 3457, 3461, 3581, 3691, 3727, 3833, 3947, 3967, 4129, 4253, 4297, 4423, 4567, 4957, 5323, 5381, 5651
Offset: 1
Examples
743 is prime. 743 - (7*4*3) = 659 is prime. 743 + (7*4*3) = 827 is prime. So, 743 is a member of this sequence.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Programs
-
Maple
A007954 := proc(n) mul(d, d=convert(n, base, 10)) end proc: isA229176 := proc(n) if isprime(n) and A007954(n) <> 0 then isprime(n+A007954(n)) and isprime(n-A007954(n)) ; simplify(%) ; else false; end if; end proc: for n from 1 to 10000 do if isA229176(n) then printf("%d,",n) ; end if; end do:
-
Mathematica
id[x_] := IntegerDigits[x]; ti[x_] := Times @@ id[x]; m=5000; Select[Range[3,m,2], PrimeQ[#] && Min[id[#]] > 0 && PrimeQ[#+ti[#]] && PrimeQ[#-ti[#]]&] (* Zak Seidov, Oct 02 2013 *) t@n_ := Block[{p = Times @@ IntegerDigits@n}, If[p == 0, {0}, n + {-p, p}]]; Select[Prime@Range@1000, AllTrue[t@#, PrimeQ] &] (* Hans Rudolf Widmer, Dec 13 2021 *)
-
PARI
forprime(p=1,10^4,d=digits(p);P=prod(i=1,#d,d[i]);if(P&&isprime(p+P)&&isprime(p-P),print1(p,", "))) \\ Derek Orr, Mar 22 2015
-
Python
import sympy from sympy import isprime def DP(n): p = 1 for i in str(n): p *= int(i) return p {print(n, end=', ') for n in range(10**4) if DP(n) and isprime(n) and isprime(n+DP(n)) and isprime(n-DP(n))} # Simplified by Derek Orr, Mar 22 2015
Comments