A216378 Numbers m such that m*10^m + 1 is a semiprime.

2, 5, 13, 28, 34, 36, 39, 111, 117, 123, 181, 184, 187

Offset

1,1

Comments

This is to A007647 as semiprimes A001358 is to primes A000040. The corresponding semiprimes are A216376 = {201, 500001, 130000000000001, 280000000000000000000000000001, ...}.

a(14) >= 414. - Daniel Suteu, Jul 09 2019

Links

Table of n, a(n) for n=1..13.

Status of 414*10^414+1 in factordb.com.

Example

a(1) = 2 because 2 * 10^2 + 1 = 201 = 3 * 67.
a(2) = 5 because  5 * 10^5 + 1 = 500001 = 3 * 166667.
a(3) = 13 because 13*10^13 + 1 = 130000000000001 = 6529 * 19911165569.
a(4) = 28 because 28 * 10^28 + 1 = 29 * 9655172413793103448275862069.

Mathematica

Select[Range[40], PrimeOmega[# 10^# + 1] == 2 &] (* Alonso del Arte, Sep 08 2012 *)

Prog

(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [1..70] | IsSemiprime(s) where s is n*10^n+1]; // Vincenzo Librandi, May 10 2014

Crossrefs

Cf. A001358, A007647, A064748, A216376.

Cf. similar sequences listed in A242203.

Sequence in context: A126656 A272794 A026522 * A225690 A193044 A122491

Adjacent sequences: A216375 A216376 A216377 * A216379 A216380 A216381

Keyword

nonn,more,hard

Author

Jonathan Vos Post, Sep 06 2012

Extensions

a(8)-a(13) from Daniel Suteu, Jul 09 2019

Status

approved