A335599 Sequence is limit_{k->oo} s_k, where s_k = s_{k-1}, s_{k-1}[k-1] + 2^(k-1), ..., s_{k-1}[end] + 2^(k-1) starting with s_0 = s_0[0..1] = 0,0.

0, 0, 1, 1, 2, 3, 3, 5, 5, 6, 7, 7, 9, 10, 11, 11, 13, 13, 14, 15, 15, 18, 19, 19, 21, 21, 22, 23, 23, 25, 26, 27, 27, 29, 29, 30, 31, 31, 35, 35, 37, 37, 38, 39, 39, 41, 42, 43, 43, 45, 45, 46, 47, 47, 50, 51, 51, 53, 53, 54, 55, 55, 57, 58, 59, 59, 61, 61

Offset

0,5

Comments

In binary 0, 0, 1, 1, 10, 11, 11, 101, 101, 110, 111, 111, 1001, 1010, 1011, 1101, 1110, 1111, 1111, 10010, 10011, 10011, 10101, ...

a(n) = m is the smallest solution to m + bitcount(m) = n or n-1. So a(n) = smaller nonzero of A228086(n) and A228086(n-1) (for n>=2). - Kevin Ryde, Jul 05 2020

Links

Table of n, a(n) for n=0..67.

Kevin Ryde, PARI/GP code and explanation, quantity "b(n)".

Formula

a(n) + bitcount(a(n)) + A334820(n) = n for n>=0.

Maple

s:= proc(n) option remember; `if`(n=0, [0, 0][], (l->
     [l[], map(x-> x+2^(n-1), l[n..-1])[]][])([s(n-1)]))
    end:
s(7);  # gives 136 = A005126(7) terms;  # Alois P. Heinz, Jul 04 2020

Mathematica

a[n_] := If[n == 0, 0,
Module[{m = n, k = Floor@Log2[n]}, m -= k + 1; While[k >= 0,
     If[BitGet[m, k] == 0, m++;
     If[BitGet[m, k] == 1, Return[m-1]]]; k--]; m]];
Table[a[n], {n, 0, 67}] (* Jean-François Alcover, May 30 2022, after Kevin Ryde *)

Prog

(PARI) a(n) = { if(n, my(k=logint(n, 2)); n-=k+1;
  while(k>=0, if(!bittest(n, k), n++; if(bittest(n, k), return(n-1))); k--));
  n; }  \\ Kevin Ryde, Jul 05 2020

Crossrefs

Cf. A005126, A334820.

Sequence in context: A023816 A353714 A159237 * A227065 A010761 A320840

Adjacent sequences: A335596 A335597 A335598 * A335600 A335601 A335602

Keyword

nonn

Author

Richard Aime Blavy, Jun 15 2020

Status

approved