A043276 a(n) = maximal run length in base-2 representation of n.

1, 1, 2, 2, 1, 2, 3, 3, 2, 1, 2, 2, 2, 3, 4, 4, 3, 2, 2, 2, 1, 2, 3, 3, 2, 2, 2, 3, 3, 4, 5, 5, 4, 3, 3, 2, 2, 2, 3, 3, 2, 1, 2, 2, 2, 3, 4, 4, 3, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 6, 6, 5, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 3, 4, 4, 3, 2, 2, 2, 1, 2, 3, 3, 2, 2, 2, 3, 3, 4, 5, 5, 4, 3, 3, 2, 2, 2, 3, 3, 2

Offset

1,3

Comments

First occurrence of k is when n=2^k-1 and there is no last occurrence. - Robert G. Wilson v, Dec 14 2008

Sequences A000975, A037969, A037970, A037971 list numbers for which a(n)=1, a(n)=2, a(n)=3, a(n)=4. - M. F. Hasler, Jul 23 2013

a(n) = max(A101211(n,k): k = 1..A005811(n)). - Reinhard Zumkeller, Dec 16 2013

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Maple

A043276 := proc(n)
    local a, rl, i ;
    if n > 0 then
        rl := 1 ;
    else
        rl := 0 ;
    end if;
    a := rl ;
    dgs := convert(n, base, 2) ;
    for i from 2 to nops(dgs) do
        if op(i, dgs) = op(i-1, dgs) then
            rl := rl+1 ;
            a := max(a, rl) ;
        else
            a := max(a, rl) ;
            rl := 1;
        end if;
    end do:
    a ;
end proc:
seq(A043276(n), n=1...80) ; # R. J. Mathar, Jun 04 2021

Mathematica

f[n_] := Max @@ Length /@ Split@IntegerDigits[n, 2]; Array[f, 105] (* Robert G. Wilson v, Dec 14 2008 *)

Prog

(PARI) A043276(n, b=2)={my(m, c=1); while(n>0, n%b==(n\=b)%b && c++ && next; m=max(m, c); c=1); m} \\ M. F. Hasler, Jul 23 2013
(PARI) a(n)=my(r, t); while(n, t=valuation(n, 2); if(t>r, r=t); n>>=t; t=valuation(n+1, 2); if(t>r, r=t); n>>=t); r \\ Charles R Greathouse IV, Nov 02 2016
(Haskell)
a043276 = maximum . a101211_row  -- Reinhard Zumkeller, Dec 16 2013
(Python)
from itertools import groupby
def A043276(n): return max(len(list(g)) for k, g in groupby(bin(n)[2:])) # Chai Wah Wu, Mar 09 2023

Crossrefs

Cf. A043277-A043290 for base-3 to base-16 analogs.

Sequence in context: A355080 A165915 A269783 * A319416 A284559 A284583

Adjacent sequences: A043273 A043274 A043275 * A043277 A043278 A043279

Keyword

nonn,base,look

Author

Clark Kimberling

Extensions

More terms from Robert G. Wilson v, Dec 14 2008

Status

approved