A309249 Primes p such that p * (product of digits of p) - 2 is prime.

2, 3, 5, 7, 13, 73, 113, 173, 193, 197, 359, 373, 937, 1117, 1153, 1531, 1571, 1597, 1777, 1951, 1979, 3119, 3313, 3517, 3539, 3557, 3571, 5119, 5399, 5591, 5779, 7159, 7177, 7351, 7393, 7573, 7757, 7793, 7933, 7951, 9133, 9511, 9533, 9931, 9973, 11119, 11131

Offset

1,1

Comments

Except for 2, a subset of A030096. - Robert Israel, Jul 18 2019

Primes with zero as a digit are excluded. - Harvey P. Dale, Jan 02 2020

Links

Hauke Löffler, Table of n, a(n) for n = 1..1638

Example

2 is in the sequence because 2*(2) - 2 = 2 (prime);
359 is in the sequence because 359*(3*5*9) - 2 = 48463 (prime).

Mathematica

ppd2Q[n_]:=Module[{c=n Times@@IntegerDigits[n]-2}, c>0&&PrimeQ[c]]; Select[ Prime[Range[1500]], ppd2Q] (* Harvey P. Dale, Jan 02 2020 *)

Prog

(SageMath) P = Primes(); [ P.unrank(p) for p in range(1000) if is_prime( P.unrank(p) * prod([int(i) for i in str(P.unrank(p)) ] ) - 2 )]

Crossrefs

Cf. A000040, A030096, A309248.

Sequence in context: A055694 A249797 A346686 * A294727 A348352 A007311

Adjacent sequences: A309246 A309247 A309248 * A309250 A309251 A309252

Keyword

nonn,base

Author

Hauke Löffler, Jul 18 2019

Status

approved