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 A245017 Numbers k such that (product of digits of k) + 1 and (product of digits of k)^2 + 1 are both prime. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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, 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

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Last modified September 23 11:23 EDT 2020. Contains 337310 sequences. (Running on oeis4.)