A038374 Length of longest contiguous block of 1's in binary expansion of n.

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

Offset

1,3

Links

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

Index entries for sequences related to binary expansion of n

Formula

a(n) >= A089309(n). a(n) >= A089310(n). a(2^i)=1. a(2^i-1)=i. - R. J. Mathar, Jun 15 2006

May be defined by the recurrence given in A245196, taking G(n)=n+1 (n>=0) and m=1. - N. J. A. Sloane, Jul 25 2014

Example

a(157) = 3 because 157 in base 2 is 10011101 and longest contiguous block of 1's is of length 3.
May be arranged into blocks of lengths 1, 2, 4, 8, 16, ...:
1,
1, 2,
1, 1, 2, 3,
1, 1, 1, 2, 2, 2, 3, 4,
1, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 2, 3, 3, 4, 5,
1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 2, 2, 3, 4, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 6,
... - N. J. A. Sloane, Jul 25 2014

Maple

A038374 := proc(n) local nshft, thisr, resul; nshft := n ; resul :=0 ; thisr :=0 ; while nshft > 0 do if nshft mod 2 <> 0 then thisr := thisr+1 ; else resul := max(resul, thisr) ; thisr := 0 ; fi ; nshft := floor(nshft/2) ; od ; resul := max(resul, thisr) ; RETURN(resul) ; end : for n from 1 to 80 do printf("%d, ", A038374(n)) ; od : # R. J. Mathar, Jun 15 2006

Mathematica

Table[Max[Length/@DeleteCases[Split[IntegerDigits[n, 2]], _?(MemberQ[ #, 0] &)]], {n, 120}] (* Harvey P. Dale, Jun 10 2013 *)

Prog

(Haskell)
import Data.List (unfoldr, group)
a038374 = maximum . map length . filter ((== 1) . head) . group .
   unfoldr (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2)
-- Reinhard Zumkeller, May 01 2012
(PARI) a(n)=if (n==0, return (0)); n>>=valuation(n, 2); if(n<2, return(n)); my(e=valuation(n+1, 2)); max(e, a(n>>e)) \\ Charles R Greathouse IV, Jan 12 2014; edited by Michel Marcus, Apr 14 2019
(Python)
from itertools import groupby
def a(n): return max(len(list(g)) for k, g in groupby(bin(n)[1:]) if k=='1')
print([a(n) for n in range(1, 91)]) # Michael S. Branicky, Jul 04 2022

Crossrefs

Cf. A087117, A090000, A090001, A090002, A090003, A090050, A245196.

Sequence in context: A265754 A089309 A126387 * A284569 A272604 A284580

Adjacent sequences: A038371 A038372 A038373 * A038375 A038376 A038377

Keyword

base,easy,nonn,tabf

Author

Jeffrey Shallit

Status

approved