A330355 Starting from n: as long as the decimal representation contains a positive multiple of 3, divide the largest and leftmost such substring by 3; a(n) corresponds to the final value.

0, 1, 2, 1, 4, 5, 2, 7, 8, 1, 10, 11, 4, 11, 14, 5, 4, 17, 2, 11, 20, 7, 22, 7, 8, 25, 22, 1, 28, 7, 10, 11, 4, 11, 14, 5, 4, 17, 2, 11, 40, 41, 14, 41, 44, 5, 14, 47, 4, 41, 50, 17, 52, 17, 2, 55, 52, 11, 58, 17, 20, 7, 22, 7, 8, 25, 22, 1, 28, 7, 70, 71, 8

Offset

0,3

Comments

This sequence is a variant of A329424.

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Rémy Sigrist, PARI program for A330355

Formula

a(n) <= n with equality iff n = 0 or n belongs to A325112.

a(3^k) = 1 for any k >= 0.

Example

For n = 193:
- 193 gives 1 followed by 93/3 = 131,
- 131 gives 1 followed by 3/3 followed by 1 = 111,
- 111 gives 111/3 = 37,
- 37 gives 3/3 followed by 7 = 17,
- neither 1, 7 nor 17 are divisible by 3, so a(193) = 17.

Maple

f:= proc(n) option remember; local L, m, i, d, np1, j, s;
  L:= convert(n, base, 10);
  m:= nops(L);
  for d from m to 1 by -1 do
    for i from 1 to m-d+1 do
      s:= convert(L[i..i+d-1], `+`);
      if s > 0 and s mod 3 = 0 then
        np1:= add(L[j]*10^(j-1), j=1..i-1)+1/3*add(L[j]*10^(j-1), j=i..i+d-1);
        return procname(np1 + 10^(2+ilog10(np1)-(i+d))*add(L[j]*10^(j-1), j=i+d..m));
      fi
    od
  od;
  n
end proc:
map(f, [$0..100]); # Robert Israel, Dec 25 2019

Prog

(PARI) See Links section.

Crossrefs

Cf. A325112, A327539, A329424.

Sequence in context: A065518 A072012 A172500 * A329424 A038502 A106610

Adjacent sequences: A330352 A330353 A330354 * A330356 A330357 A330358

Keyword

nonn,base,look

Author

Rémy Sigrist, Dec 11 2019

Status

approved