A120100 Integers n for which the period of the decimal expansion of 1/n is 6.

7, 13, 14, 21, 26, 28, 35, 39, 42, 52, 56, 63, 65, 70, 77, 78, 84, 91, 104, 105, 112, 117, 126, 130, 140, 143, 154, 156, 168, 175, 182, 189, 195, 208, 210, 224, 231, 234, 252, 259, 260, 273, 280, 286, 297, 308, 312, 315, 325, 336, 350, 351, 364, 378, 385, 390

Offset: 1

Author

Gil Broussard, Aug 15 2006

Keywords

• nonn
• base

Comments

The initial terms in the sequence are multiples of either 7 or 13, but the sequence is not exclusively so. a(45) = 297 whose factors include neither 7 nor 13. Next is a(57) = 407 whose factors are 11 and 37.

Examples

			a(1) = 7 because 1/7 = 0.142857142857142857+, whose repeating decimal (142857) is 6 digits long.
a(57) = 407 because 1/407 = 0.0024570024570024+, whose repeating decimal (002457) is 6 digits long.
		

Programs

Mathematica

Transpose[Select[Table[{n,Length[RealDigits[1/n][[1,-1]]]},{n,500}],#[[2]]==6&]][[1]] (* Harvey P. Dale, Dec 04 2010 *)