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

1,1

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

Links

Table of n, a(n) for n=1..53.

Formula

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

Example

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

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]]

Crossrefs

Cf. A001358, A060284.

Sequence in context: A315434 A315435 A315436 * A141352 A276973 A248351

Adjacent sequences: A193883 A193884 A193885 * A193887 A193888 A193889

Keyword

nonn,base,hard

Author

Michel Lagneau, Aug 07 2011

Extensions

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

Status

approved