A245017 Numbers k such that (product of digits of k) + 1 and (product of digits of k)^2 + 1 are both prime.

1, 2, 4, 6, 11, 12, 14, 16, 21, 22, 23, 25, 28, 32, 41, 44, 49, 52, 58, 61, 66, 82, 85, 94, 111, 112, 114, 116, 121, 122, 123, 125, 128, 132, 141, 144, 149, 152, 158, 161, 166, 182, 185, 194, 211, 212, 213, 215, 218, 221, 224, 229, 231, 236, 242, 245, 251, 254, 263, 279, 281, 292

Offset

1,2

Comments

A number k is a term of this sequence iff A007954(k) and A007954(k)^2 are both in A006093.

This sequence is infinite. With any number a(n), you can add infinitely many 1's to its decimal representation. E.g., 82 is in this sequence, so 821, 812, 1182, 18112, 81211, etc. are also terms of this sequence.

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Example

(9*4) + 1 = 37 is prime and (9*4)^2 + 1 = 1297 is prime. Thus 94 is a term of this sequence.

Mathematica

bpQ[n_]:=Module[{c=Times@@IntegerDigits[n]}, AllTrue[{c+1, c^2+1}, PrimeQ]]; Select[Range[300], bpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 09 2019 *)

Prog

(PARI) for(n=1, 10^3, d=digits(n); p=prod(i=1, #d, d[i]); if(ispseudoprime(p+1) && ispseudoprime(p^2 + 1), print1(n, ", ")))

Crossrefs

Cf. A007954, A009994, A081988, A244748.

Sequence in context: A324333 A081988 A244748 * A300149 A171921 A030783

Adjacent sequences: A245014 A245015 A245016 * A245018 A245019 A245020

Keyword

nonn,base

Author

Derek Orr, Jul 12 2014

Status

approved