A244661 Beastly reciprocals, or numbers n such that digitsum(1/n) = 666.

149, 298, 596, 646, 745, 1192, 1490, 1615, 2119, 2584, 2980, 3109, 3725, 3878, 5960, 6218, 6357, 6460, 7106, 7294, 7450, 8476, 9262, 9868, 10941, 11627, 11634, 11920, 12436, 14535, 14900, 15049, 15545, 16150, 18625, 21190, 22718, 23256, 23902, 24872, 24915

Offset: 1

Author

Anthony Sand, Jul 04 2014

Keywords

• nonn
• base

Comments

149 is a full reptend prime (see A001913), hence the sum of the decimal digits of 1/149 is 9 * 148 / 2 = 666.

From Robert G. Wilson v, Aug 16 2014: (Start)

If n is present, so is 10n.

If n is present then A003592*n is possibly present.

Primitives are: 149, 646, 1615, 2119, 3109, 3878, 7294, 9262, 9868, 10941, …, .

Palindromes: 646, 1525251, 2062602, …, .

Primes: 149, 3109, 111149, 351391, …, .

(End)

Examples

			If digitsum(1/n) sums the decimal digits of 1/n up to the point at which they recur or terminate, then digitsum(1/149) = 666 = 0 + 0 + 6 + 7 + 1 + 1 + 4 + 0 + 9 + 3 + 9 + 5 + 9 + 7 + 3 + 1 + 5 + 4 + 3 + 6 + 2 + 4 + 1 + 6 + 1 + 0 + 7 + 3 + 8 + 2 + 5 + 5 + 0 + 3 + 3 + 5 + 5 + 7 + 0 + 4 + 6 + 9 + 7 + 9 + 8 + 6 + 5 + 7 + 7 + 1 + 8 + 1 + 2 + 0 + 8 + 0 + 5 + 3 + 6 + 9 + 1 + 2 + 7 + 5 + 1 + 6 + 7 + 7 + 8 + 5 + 2 + 3 + 4 + 8 + 9 + 9 + 3 + 2 + 8 + 8 + 5 + 9 + 0 + 6 + 0 + 4 + 0 + 2 + 6 + 8 + 4 + 5 + 6 + 3 + 7 + 5 + 8 + 3 + 8 + 9 + 2 + 6 + 1 + 7 + 4 + 4 + 9 + 6 + 6 + 4 + 4 + 2 + 9 + 5 + 3 + 0 + 2 + 0 + 1 + 3 + 4 + 2 + 2 + 8 + 1 + 8 + 7 + 9 + 1 + 9 + 4 + 6 + 3 + 0 + 8 + 7 + 2 + 4 + 8 + 3 + 2 + 2 + 1 + 4 + 7 + 6 + 5 + 1.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..546

Crossrefs

Cf. A048997, A238104, A051003, A001913.

Programs

Mathematica

fQ[n_] := Total[ RealDigits[ 1/n, 10][[1, 1]]] == 666;  Select[ Range@ 25000, fQ ] (* Robert G. Wilson v, Aug 16 2014 *)