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
Examples
(9*4) + 1 = 37 is prime and (9*4)^2 + 1 = 1297 is prime. Thus 94 is a term of this sequence.
Links
- Jens Kruse Andersen, Table of n, a(n) for n = 1..10000
Programs
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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 *) -
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,", ")))
Comments