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

1,1

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Union of A092518 and A056709.

Cf. A225303.

Sequence in context: A097436 A063980 A046124 * A092518 A355983 A110584

Adjacent sequences: A157674 A157675 A157676 * A157678 A157679 A157680

Keyword

nonn,base

Author

Kyle D. Balliet, Mar 04 2009

Extensions

More terms from Emeric Deutsch, Mar 08 2009

Status

approved