

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
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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

Table of n, a(n) for n=1..15.


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

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



