A242226 Numbers that can be written as a sum of numbers using only nonzero decimal digits in ascending order.

45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 252, 261, 270, 279, 288, 315, 324, 333, 342, 378, 387, 396, 432, 441, 450, 459, 486, 495, 504, 513, 549, 558, 567, 576, 594, 603, 612, 621, 630, 666

Offset

1,1

Comments

The sequence is divisible by 9 and contains 187 terms. The first term is 45 = 1+2+...+9, the last term is 1+23456789 = 23456790.

The decomposition is not unique, for example 666 = 1+2+3+4+567+89 = 123+456+78+9.

Links

Michel Lagneau, Table of n, a(n) for n = 1..187

Michel Lagneau, decompositions of the numbers

Example

45 = 1+2+3+4+5+6+7+8+9;
54 = 12+3+4+5+6+7+8+9;
63 = 1+23+4+5+6+7+8+9;
72 = 1+2+34+5+6+7+8+9;
81 = 1+2+3+45+6+7+8+9 = 12+34+5+6+7+8+9;
90 = 1+2+3+4+56+7+8+9 = 12+3+45+6+7+8+9;
99 = 1+2+3+4+5+67+8+9 = 12+3+4+56+7+8+9 = 1+23+45+6+7+8+9.

Maple

g:= proc(i, j) option remember;
      `if`(i=j, {i}, {parse(cat(seq(h, h=i..j))),
       seq(seq(seq(x+y, y=g(h+1, j)), x=g(i, h)), h=i..j-1)})
    end:
sort([(g(1, 9) minus {123456789})[]])[];  # Alois P. Heinz, May 09 2014

Crossrefs

Cf. A008591.

Sequence in context: A345482 A295802 A242267 * A335375 A039423 A043246

Adjacent sequences: A242223 A242224 A242225 * A242227 A242228 A242229

Keyword

nonn,base,fini,full

Author

Michel Lagneau, May 08 2014

Status

approved