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A309358
Numbers k such that 10^k + 1 is a semiprime.
1
4, 5, 6, 7, 8, 19, 31, 53, 67, 293, 586, 641, 922, 2137, 3011
OFFSET
1,1
COMMENTS
a(16) > 12000.
10^k + 1 is composite unless k is a power of 2, and it can be conjectured that it is composite for all k > 2, cf. A038371 and A185121. - M. F. Hasler, Jul 30 2019
Suppose k is odd. Then k is a term if and only if (10^k+1)/11 is prime. - Chai Wah Wu, Jul 31 2019
EXAMPLE
a(1) = 4 because 10^4 + 1 = 10001 = 73*137.
MATHEMATICA
Select[Range[200], Plus@@Last/@FactorInteger[10^# + 1] == 2 &] (* Vincenzo Librandi, Jul 31 2019 *)
PROG
(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..200] | IsSemiprime(s) where s is 10^n+1]; // Vincenzo Librandi, Jul 31 2019
CROSSREFS
Odd terms in sequence: A001562.
Sequence in context: A280682 A140293 A075341 * A143789 A068521 A196697
KEYWORD
nonn,more,hard
AUTHOR
Hugo Pfoertner, Jul 29 2019
STATUS
approved