A244748 Numbers k such that (product of digits of k)^2 + 1 is prime.

1, 2, 4, 6, 11, 12, 14, 16, 21, 22, 23, 25, 27, 28, 32, 38, 41, 44, 45, 46, 49, 52, 54, 58, 61, 64, 66, 69, 72, 78, 82, 83, 85, 87, 94, 96, 111, 112, 114, 116, 121, 122, 123, 125, 127, 128, 132, 138, 141, 144, 145, 146, 149, 152, 154, 158, 161, 164, 166, 169, 172, 178, 182, 183

Offset: 1

Author

Derek Orr, Jul 12 2014

Keywords

• nonn
• base
• easy

Comments

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

This sequence is infinite. With any number a(n), you can add infinitely many 1's to its decimal representation. E.g., 85 is in this sequence, so 185, 815, 851, 1185, 1815, 18115, etc. are terms as well.

Examples

			(7*2)^2 + 1 = 197 is prime. Thus 72 is a term of this sequence.
		

Links

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

Crossrefs

Cf. A081988, A007954.

Programs

PARI

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

Extensions

Corrected by Jens Kruse Andersen, Jul 13 2014