A054465 - OEIS

%I #14 Nov 18 2018 10:33:10

%S 4,20,349,474,3999,4624,5000,35624,390624,499999,1609375,27109375,

%T 40000000,137109375,149999999,3000000000,4787109375,6787109375,

%U 24999999999,200000000000,281787109375,1581787109375,3499999999999

%N Numbers k such that Sum_{j=1..k} d(j) is an integer where d(j) is the decimal fraction 0.2j (e.g., d(14) = 0.28).

%C Conjecture: the number of k > 0 such that a(k) <= n is asymptotic to C*log(n), C > 0.

%C Also, solutions x to the quadratic modular equation: x^2 + x + c ==0 (mod 10^a) where c = ((8-18*a)*10^a + 10^(2*a))/40, such that ceiling(10^(a-1)/2) <= x <= (10^a/2)-1, a=1,2,... - Herman Jamke (hermanjamke(AT)fastmail.fm), May 06 2007

%e 0.2 + 0.4 + 0.6 + 0.8 = 2, hence 4 is in the sequence.

%t s = 0; Do[s += (2*n)/10^Length[IntegerDigits[2*n]]; If[IntegerQ[s], Print[n]], {n, 1, 10^6}] (* _Ryan Propper_, Jul 30 2005 *)

%K base,nonn

%O 1,1

%A _Benoit Cloitre_, Aug 30 2003

%E More terms from _Ryan Propper_, Jul 30 2005

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 06 2007