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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A023816 A353714 A159237 * A227065 A010761 A320840
KEYWORD
nonn
AUTHOR
Richard Aime Blavy, Jun 15 2020
STATUS
approved

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Last modified May 29 12:05 EDT 2024. Contains 372940 sequences. (Running on oeis4.)