A157677 Primes p such that p + (product of digits of p) is also prime.

23, 29, 61, 67, 83, 101, 103, 107, 109, 163, 233, 239, 283, 293, 307, 347, 349, 401, 409, 431, 439, 443, 449, 499, 503, 509, 563, 569, 601, 607, 613, 617, 619, 653, 659, 677, 683, 701, 709, 743, 809, 907, 929, 941, 1009, 1013, 1019, 1021, 1031, 1033, 1039

Offset: 1

Author

Kyle D. Balliet, Mar 04 2009

Keywords

• nonn
• base

Comments

If p contains a zero, then p is trivially a member.

Examples

			83 is prime, and 83 + 8*3 = 89 which is also prime. 103 is prime, and 103 + 1*0*3 = 103 is also prime. Thus 89 and 103 are members.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Union of A092518 and A056709.

Cf. A225303.

Programs

Maple

a := proc (n) local nn: nn := convert(ithprime(n), base, 10): if isprime(ithprime(n)+product(nn[j], j = 1 .. nops(nn))) = true then ithprime(n) else end if end proc: seq(a(n), n = 1 .. 180); # Emeric Deutsch, Mar 08 2009

Mathematica

Select[Prime[Range[175]], PrimeQ[# + Times @@ IntegerDigits[#]] &] (* Jayanta Basu, Apr 22 2013 *)

PARI

dprod(n)=n=digits(n); prod(i=1,#n,n[i])
is(n)=isprime(n) && isprime(n+dprod(n)) \\ Charles R Greathouse IV, Dec 27 2013

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Apr 22 2013

Extensions

More terms from Emeric Deutsch, Mar 08 2009