A216376 Semiprimes of the form n*10^n + 1.

201, 500001, 130000000000001, 280000000000000000000000000001, 340000000000000000000000000000000001, 36000000000000000000000000000000000001, 39000000000000000000000000000000000000001

Offset: 1

Author

Jonathan Vos Post, Sep 06 2012

Keywords

• nonn
• hard

Comments

This is to A216347 as semiprimes A001358 are to primes A000040. The corresponding n are 2, 5, 13, 28, 34, 36, 39, ... (A216378).

a(14) >= 414*10^414 + 1. - Hugo Pfoertner, Jul 28 2019

Examples

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

Links

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

Crossrefs

Cf. A001358, A064748, A216347, A216378.

Programs

Magma

IsSemiprime:= func; [s: n in [1..40] | IsSemiprime(s) where s is n*10^n + 1]; // Vincenzo Librandi, Sep 22 2012

Mathematica

SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; Select[Table[n*10^n + 1, {n, 50}], SemiPrimeQ[#] &] (* T. D. Noe, Sep 07 2012 *)
Select[Table[n*10^n + 1, {n, 50}], PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 22 2012 *)

Formula

semiprimes in A064748.