A244592 Numbers n such that n equals the partial or complete sum of the decimal digits of 1/n, up to the point at which the digits recur or terminate.

3, 7, 8, 13, 14, 34, 43, 49, 51, 76, 83, 92, 94, 98, 103, 109, 113, 127, 139, 141, 169, 177, 179, 181, 194, 218, 229, 283, 323, 338, 367, 394, 397, 401, 437, 524, 526, 537, 579, 587, 626, 659, 661, 673, 674, 687, 701, 719, 724, 743, 767, 769, 802, 823, 838

Offset: 1

Author

Anthony Sand, Jul 01 2014

Keywords

• nonn
• base

Comments

The digits summed are those before the decimal expansion recurs or terminates. Otherwise reciprocals that supply a recurrent 1, like 1/9 = 0.111... or 1/99 = 0.010101..., would always produce a sum equal to n from sufficient terms of the reciprocal.

Examples

			1/3 = 0.3... and 3 = 0 + 3.
1/7 = 0.142857... and 7 = 1 + 4 + 2.
1/8 = 0.125 and 8 = 1 + 2 + 5.
1/13 = 0.0769230... and 13 = 7 + 6.
1/14 = 0.0714285... and 14 = 7 + 1 + 4 + 2.
1/34 = 0.02941176470588235... and 34 = 2 + 9 + 4 + 1 + 1 + 7 + 6 + 4.
		

Crossrefs

Cf. A048997.