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).

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

Links

Table of n, a(n) for n=1..23.

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

Adjacent sequences: A054462 A054463 A054464 * A054466 A054467 A054468

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