A227948 Zeroless numbers n such that n + (product of digits of n) and n - (product of digits of n) are prime.

21, 23, 27, 29, 81, 83, 253, 293, 299, 343, 347, 349, 431, 437, 439, 471, 473, 477, 529, 623, 653, 659, 677, 743, 893, 1123, 1219, 1253, 1257, 1297, 1423, 1489, 1521, 1523, 1529, 1587, 1589, 1657, 1763, 1853, 1867, 1927, 2151, 2167, 2239, 2277, 2279, 2321, 2327, 2329, 2377, 2413, 2443, 2459, 2467, 2497, 2543, 2569

Offset: 1

Author

Derek Orr, Oct 04 2013

Keywords

• nonn
• base
• easy

Comments

Intersection of A157676 and A229221 (without the primes containing zero digits).

Examples

			29 - 2*9 = 11 (prime) and 29 + 2*9 = 47 (prime) so 29 is a member of this sequence.
743 - 7*4*3 = 659 (prime) and 743 + 7*4*3 = 827 (prime) so 743 is a member of this sequence.
		

Crossrefs

Cf. A157676, A229221, A007954, A052382.

Programs

PARI

for(n=1,5000,d=digits(n);p=prod(i=1,#d,d[i]);if(p&&isprime(n+p)&&isprime(n-p),print1(n,", "))) \\ Derek Orr, Apr 05 2015

Python

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(5000) if DP(n) and isprime(n+DP(n)) and isprime(n-DP(n))}
## Simplified by Derek Orr, Apr 05 2015

Extensions

More terms from Derek Orr, Apr 05 2015