cp's OEIS Frontend

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

%I A244661 #19 Aug 21 2014 22:20:47
%S A244661 149,298,596,646,745,1192,1490,1615,2119,2584,2980,3109,3725,3878,
%T A244661 5960,6218,6357,6460,7106,7294,7450,8476,9262,9868,10941,11627,11634,
%U A244661 11920,12436,14535,14900,15049,15545,16150,18625,21190,22718,23256,23902,24872,24915
%N A244661 Beastly reciprocals, or numbers n such that digitsum(1/n) = 666.
%C A244661 149 is a full reptend prime (see A001913), hence the sum of the decimal digits of 1/149 is 9 * 148 / 2 = 666.
%C A244661 From _Robert G. Wilson v_, Aug 16 2014: (Start)
%C A244661 If n is present, so is 10n.
%C A244661 If n is present then A003592*n is possibly present.
%C A244661 Primitives are: 149, 646, 1615, 2119, 3109, 3878, 7294, 9262, 9868, 10941, …, .
%C A244661 Palindromes: 646, 1525251, 2062602, …, .
%C A244661 Primes: 149, 3109, 111149, 351391, …, .
%C A244661 (End)
%H A244661 Robert G. Wilson v, <a href="/A244661/b244661.txt">Table of n, a(n) for n = 1..546</a>
%e A244661 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.
%t A244661 fQ[n_] := Total[ RealDigits[ 1/n, 10][[1, 1]]] == 666;  Select[ Range@ 25000, fQ ] (* _Robert G. Wilson v_, Aug 16 2014 *)
%Y A244661 Cf. A048997, A238104, A051003, A001913.
%K A244661 nonn,base
%O A244661 1,1
%A A244661 _Anthony Sand_, Jul 04 2014