A245017 - OEIS

%I #22 Nov 09 2019 12:47:57

%S 1,2,4,6,11,12,14,16,21,22,23,25,28,32,41,44,49,52,58,61,66,82,85,94,

%T 111,112,114,116,121,122,123,125,128,132,141,144,149,152,158,161,166,

%U 182,185,194,211,212,213,215,218,221,224,229,231,236,242,245,251,254,263,279,281,292

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

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

%C 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.

%H Jens Kruse Andersen, <a href="/A245017/b245017.txt">Table of n, a(n) for n = 1..10000</a>

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

%t 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 *)

%o (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,", ")))

%Y Cf. A007954, A009994, A081988, A244748.

%K nonn,base

%O 1,2

%A _Derek Orr_, Jul 12 2014