A269306 a(n+1) is the smallest integer such that the difference between its digital sum and the digital sum of a(n) is n.

0, 1, 3, 6, 19, 69, 399, 1999, 9999, 99999, 1999999, 39999999, 699999999, 19999999999, 699999999999, 39999999999999, 1999999999999999, 99999999999999999, 9999999999999999999, 1999999999999999999999

Offset

1,3

Comments

The digital sums are the triangular numbers A000217. A similar idea is in A268605 (thanks to Michel Marcus for this comment).

Links

Table of n, a(n) for n=1..20.

Example

a(8) = 1999 and 1 + 9 + 9 + 9 = 28; so a(9) = 9999 because 9 + 9 + 9 + 9 = 36 and 36 - 28 = 8.

Prog

(Python)
s = 0
for i in range(1, 100):
..alfa = ""
..k = i + s
..s = k
..while k > 9:
....alfa = alfa + "9"
....k = k - 9
..alfa = str(k)+alfa
..print alfa
(PARI) findnext(x, k) = {sx = sumdigits(x); y = 1; while (sumdigits(y) - sx != k, y++); y; }
lista(nn) = {print1(x = 0, ", "); for (k=1, nn, y = findnext(x, k); print1(y, ", "); x = y; ); }

Crossrefs

Cf. A000217, A268605.

Sequence in context: A184937 A215817 A365119 * A326317 A306522 A290784

Adjacent sequences: A269303 A269304 A269305 * A269307 A269308 A269309

Keyword

nonn,base

Author

Francesco Di Matteo, Feb 23 2016

Status

approved