A193886 Numbers n such that the decimal form of the period of 1/n is semiprime (omit any trailing zeros from the period).

6, 11, 15, 24, 54, 60, 66, 81, 96, 110, 111, 123, 135, 144, 150, 165, 216, 225, 240, 303, 352, 375, 384, 396, 477, 528, 540, 600, 660, 666, 711, 717, 738, 792, 810, 813, 960, 1056, 1100, 1110, 1111, 1230, 1350, 1440, 1500, 1536, 1650, 1665, 1728, 1818, 1845, 2043, 2079

Offset: 1

Author

Michel Lagneau, Aug 07 2011

Keywords

• nonn
• base
• hard

Comments

The sequence is infinite: if n is in the sequence, then n*10^m, m = 1,2,... are in the sequence.

The subsequence of semiprimes k such that the decimal form of the period of 1/k is semiprime begins: 6, 15, 111, 123, 303, 717, 813, 1111. - Jonathan Vos Post, Oct 22 2011

Examples

			54 is in the sequence because 1/54 = 0.01851851851851... and 185 = 5*37 is semiprime.
110 is in the sequence because 1/110 = 0.009090909090..., with period "90", and 9 is a semiprime. - _Harvey P. Dale_ and _N. J. A. Sloane_, Sep 07 2020
		

Crossrefs

Cf. A001358, A060284.

Programs

Mathematica

Reap[Do[p=RealDigits[1/k][[1,-1]];If[Head[p]===List,While[p[[-1]]==0,p=Most[p]];If[PrimeOmega[FromDigits[p]]==2,Sow[k]]],{k,120}]][[2,1]]

Formula

{ n : A060284(n) in {A001358} }.

Extensions

a(12)-a(53) from Alois P. Heinz, Aug 09 2011