login
A054465
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).
0
4, 20, 349, 474, 3999, 4624, 5000, 35624, 390624, 499999, 1609375, 27109375, 40000000, 137109375, 149999999, 3000000000, 4787109375, 6787109375, 24999999999, 200000000000, 281787109375, 1581787109375, 3499999999999
OFFSET
1,1
COMMENTS
Conjecture: the number of k > 0 such that a(k) <= n is asymptotic to C*log(n), C > 0.
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
EXAMPLE
0.2 + 0.4 + 0.6 + 0.8 = 2, hence 4 is in the sequence.
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A358544 A167002 A227005 * A118713 A303630 A257547
KEYWORD
base,nonn
AUTHOR
Benoit Cloitre, Aug 30 2003
EXTENSIONS
More terms from Ryan Propper, Jul 30 2005
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 06 2007
STATUS
approved