A173394 Positions of powers of 2 in A084680.

1, 3, 9, 11, 17, 33, 51, 73, 99, 101, 137, 153, 187, 219, 257, 303, 353, 411, 449, 561, 641, 657, 771, 803, 909, 1059, 1111, 1233, 1241, 1347, 1409, 1507, 1683, 1717, 1923, 2313, 2329, 2409, 2827, 3177, 3333, 3723, 3883, 4041, 4227, 4369, 4521, 4939

Offset: 1

Author

Michel Lagneau, Feb 17 2010

Keywords

• nonn

Comments

The n where the decimal expansion of 1/n has a period length which is a power of 2.

Examples

			Period of 1/3 = 1. Period of 1/9 = 2. Period of 1/73 = 8. Period of 1/353 = 32.
		

References

• J. W. L. Glaisher, On circulating decimals, Proc. Camb. Phil. Soc., 3 (1878), 185-206.
• D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, pp. 7-12.

Links

• Eric Weisstein's World of Mathematics, Decimal Expansion.

Crossrefs

Cf. A002329.

Programs

Maple

A084680 := proc(n) if gcd(n,10) <> 1 then 0 ; elif n = 1 then 1 ; else numtheory[order](10,n) ; end if; end proc:
isA000079 := proc(n) if n = 1 then true; elif n >=1 then numtheory[factorset](n) = {2} ; else false; end if; end proc:
for n from 1 to 5000 do if isA000079(A084680(n)) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Mar 10 2010

Formula

{n: A084680(n) in A000079}.

Extensions

Missing numbers -those where A084680(n)>1000- inserted - R. J. Mathar, Mar 10 2010