A298359 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, Sum_{k = 1..n} 10^(k-1) * a(k) can be computed without carry in decimal base.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 60, 61, 62, 63, 70, 71, 72, 80, 81, 90, 100, 19, 37, 46, 55, 64, 73, 82, 91, 110, 28, 56, 74

Offset: 1

Author

Rémy Sigrist, Jan 17 2018

Keywords

• nonn
• base

Comments

More informally: write the terms in decimal under each other, right-justified; the digits on each diagonal in downwards direction sum at most to 9.

The corresponding sequence for base 2 is A094958.

See also A298425 for a similar sequence.

Examples

			The first terms, alongside 10^(n-1) * a(n), are:
  n   a(n)  10^(n-1) * a(n)
  --  ----  -------------------
   1   1                      1
   2   2                     20
   3   3                    300
   4   4                   4000
   5   5                  50000
   6   6                 600000
   7   7                7000000
   8   8               80000000
   9   9              900000000
  10  10            10000000000
  11  11           110000000000
  12  12          1200000000000
  13  13         13000000000000
  14  14        140000000000000
  15  15       1500000000000000
  16  16      16000000000000000
  17  17     170000000000000000
  18  18    1800000000000000000
  19  20   20000000000000000000
  20  21  210000000000000000000
The terms on the third column can be summed without carry in decimal base.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A298359

Crossrefs

Cf. A094958, A298425.

Programs

PARI

See Links section.