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

1,2

Comments

This sequence is a decimal variant of A238757.

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Formula

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

Example

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

Prog

(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)))

Crossrefs

Cf. A007953, A238757, A252022.

Sequence in context: A080897 A117383 A047455 * A202426 A039002 A295393

Adjacent sequences: A336190 A336191 A336192 * A336194 A336195 A336196

Keyword

nonn,base,look

Author

Rémy Sigrist, Jul 11 2020

Status

approved