

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.


1



0, 1, 3, 6, 19, 69, 399, 1999, 9999, 99999, 1999999, 39999999, 699999999, 19999999999, 699999999999, 39999999999999, 1999999999999999, 99999999999999999, 9999999999999999999, 1999999999999999999999
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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: A058818 A184937 A215817 * A326317 A306522 A290784
Adjacent sequences: A269303 A269304 A269305 * A269307 A269308 A269309


KEYWORD

nonn,base


AUTHOR

Francesco Di Matteo, Feb 23 2016


STATUS

approved



