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

Author

Rémy Sigrist, Dec 11 2019

Keywords

• nonn
• base
• look

Comments

This sequence is a variant of A329424.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, PARI program for A330355

Crossrefs

Cf. A325112, A327539, A329424.

Programs

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

PARI

See Links section.

Formula

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

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