A054464 Numbers n such that Sum_{k=1..n} d(k) is an integer where d(k) is the decimal fraction 0.k (e.g. d(999)=0.999).

4, 34, 90, 175, 800, 2999, 3624, 30624, 60000, 390624, 499999, 4000000, 8890624, 17109375, 69999999, 200000000, 2787109375, 8999999999, 81787109375, 900000000000, 1918212890624, 1999999999999, 70000000000000, 89918212890624, 399999999999999, 659918212890624

Offset

1,1

Comments

For d >=2, the m with d digits are the solutions of x^2 + x - 9*10^(d-1)*d - 10^(d-1) == 0 (mod 2*10^d) with 10^(d-1) <= x < 10^d. - Robert Israel, Aug 08 2016

Links

Robert Israel, Table of n, a(n) for n = 1..1792

Example

0.1+0.2+0.3+0.4 = 1 hence 4 is in the sequence.

Maple

F:= proc(d) local x, S;
  S:= map(t -> subs(t, x), [msolve(x^2 + x - 9*10^(d-1)*d - 10^(d-1), 2*10^d)]);
  op(sort(select(t -> t >= 10^(d-1) and t < 10^d, S)))
end proc:
4, seq(F(d), d=2..30); # Robert Israel, Aug 08 2016

Mathematica

Flatten[Position[IntegerQ /@ Table[ Sum[10^-Length[IntegerDigits[i]]*i, {i, j}], {j, 1, 50000}], True]] (from Vit Planocka)

Crossrefs

See A275572 for an essentially equivalent sequence.

See A275623 for the corresponding sums.

Sequence in context: A281827 A284812 A053902 * A002101 A241231 A297715

Adjacent sequences: A054461 A054462 A054463 * A054465 A054466 A054467

Keyword

base,nonn

Author

Benoit Cloitre, Aug 30 2003

Extensions

One more term from Vit Planocka (planocka(AT)mistral.cz), Sep 24 2003

Terms a(9) - a(15) from John W. Layman, Jun 03 2005

a(16) - a(18) from Ryan Propper, Aug 25 2005

Status

approved