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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

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

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