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A157677 Primes p such that p + (product of digits of p) is also prime. 7
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 (list; graph; refs; listen; history; text; internal format)
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 A110584 A115396

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

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Last modified May 24 14:18 EDT 2022. Contains 354037 sequences. (Running on oeis4.)