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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 (list; graph; refs; listen; history; text; internal format)
 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 LINKS 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; [n: n in [2..200] | IsSemiprime(s) where s is 10^n+1]; // Vincenzo Librandi, Jul 31 2019 CROSSREFS Cf. A003021, A038371, A046413, A057934, A062397, A092559. Odd terms in sequence: A001562. Sequence in context: A280682 A140293 A075341 * A143789 A068521 A196697 Adjacent sequences:  A309355 A309356 A309357 * A309359 A309360 A309361 KEYWORD nonn,more,hard AUTHOR Hugo Pfoertner, Jul 29 2019 STATUS approved

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Last modified April 6 18:35 EDT 2020. Contains 333286 sequences. (Running on oeis4.)