A336193 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, n + a(n) can be computed without carry in base 10.

1, 2, 3, 4, 10, 11, 12, 20, 30, 5, 6, 7, 13, 14, 21, 22, 31, 40, 50, 8, 15, 16, 23, 24, 32, 33, 41, 51, 60, 9, 17, 25, 26, 34, 42, 43, 52, 61, 100, 18, 27, 35, 36, 44, 53, 101, 102, 110, 120, 19, 28, 37, 45, 103, 104, 111, 112, 121, 130, 29, 38, 105, 106, 113

Offset: 1

Author

Rémy Sigrist, Jul 11 2020

Keywords

• nonn
• base
• look

Comments

This sequence is a decimal variant of A238757.

This sequence is a self-inverse permutation of the natural numbers.

Examples

			The first terms, alongside n + a(n), are:
  n   a(n)  n+a(n)
  --  ----  ------
   1     1       2
   2     2       4
   3     3       6
   4     4       8
   5    10      15
   6    11      17
   7    12      19
   8    20      28
   9    30      39
  10     5      15
  11     6      17
  12     7      19
  13    13      26
  14    14      28
  15    21      36
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A007953, A238757, A252022.

Programs

PARI

s=0; for (n=1, 64, for (v=1, oo, if (!bittest(s,v) && sumdigits(n+v)==sumdigits(n)+sumdigits(v), print1(v", "); s+=2^v; break)))

Formula

A007953(n + a(n)) = A007953(n) + A007953(a(n)).