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A193886
Numbers n such that the decimal form of the period of 1/n is semiprime (omit any trailing zeros from the period).
0
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
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
Sequence in context: A315434 A315435 A315436 * A141352 A276973 A248351
KEYWORD
nonn,base,hard
AUTHOR
Michel Lagneau, Aug 07 2011
EXTENSIONS
a(12)-a(53) from Alois P. Heinz, Aug 09 2011
STATUS
approved