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

Author

Francesco Di Matteo, Feb 23 2016

Keywords

• nonn
• base

Comments

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

Examples

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

Crossrefs

Cf. A000217, A268605.

Programs

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; ); }

Python

s = 0
for i in range(0, 100):
  alfa = ""
  k = i + s
  s = k
  while k > 9:
    alfa = alfa + "9"
    k = k - 9
  alfa = str(k) + alfa
  print(alfa)