The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A087117

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A087117

Number of zeros in the longest string of consecutive zeros in the binary representation of n.
(history; published version)

#31 by Charles R Greathouse IV at Thu Apr 14 16:23:15 EDT 2022

STATUS

editing

approved

#30 by Charles R Greathouse IV at Wed Apr 06 22:04:02 EDT 2022

PROG

(PARI) h(n)=if(n<2, return(0)); my(k=valuation(n, 2)); if(k, max(h(n>>k), k), n++; n>>=valuation(n, 2); h(n-1))

a(n)=if(n, h(n), 1) \\ Charles R Greathouse IV, Apr 06 2022

KEYWORD

nonn,base,easy

STATUS

approved

editing

Discussion

Thu Apr 14

01:53

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A087117 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

#29 by Susanna Cuyler at Fri Apr 10 08:16:00 EDT 2020

STATUS

proposed

approved

#28 by Gus Wiseman at Fri Apr 10 07:12:53 EDT 2020

STATUS

editing

proposed

#27 by Gus Wiseman at Fri Apr 10 07:05:49 EDT 2020

CROSSREFS

Cf. A029931, A048793, A061395, A087117, A228351, A328594, A333217, A333218, A333219, A333632, A333767, A333768.

#26 by Gus Wiseman at Thu Apr 09 23:56:25 EDT 2020

COMMENTS

The k-th composition in standard order (row k of A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. Then a(k) is the maximum part of this composition, minus one. The maximum part is A333766(k). - Gus Wiseman, Apr 09 2020

FORMULA

For n > 0, a(n) = A333766(n) - 1. - Gus Wiseman, Apr 09 2020

CROSSREFS

Positions of zeros are A000225.

Positions of terms <= 1 are A003754.

Positions of terms > 0 are A062289.

Positions of first appearances are A131577.

The version for prime indices is A252735.

The proper maximum is A333766.

The version for minimum is A333767.

Maximum prime index is A061395.

All of the following pertain to compositions in standard order (A066099):

- Length is A000120.

- Sum is A070939.

- Runs are counted by A124767.

- Strict compositions are A233564.

- Constant compositions are A272919.

- Runs-resistance is A333628.

- Weakly decreasing compositions are A114994.

- Weakly increasing compositions are A225620.

- Strictly decreasing compositions are A333255.

- Strictly increasing compositions are A333256.

Cf. A029931, A048793, A061395, A087117, A228351, A328594, A333217, A333218, A333219, A333632, A333767, A333768.

STATUS

approved

editing

#25 by Harvey P. Dale at Tue Sep 05 18:08:56 EDT 2017

STATUS

editing

approved

#24 by Harvey P. Dale at Tue Sep 05 18:08:52 EDT 2017

MATHEMATICA

nz[n_]:=Max[Length/@Select[Split[IntegerDigits[n, 2]], MemberQ[#, 0]&]]; Array[nz, 110, 0]/.-\[Infinity]->0 (* Harvey P. Dale, Sep 05 2017 *)

STATUS

approved

editing

#23 by Joerg Arndt at Fri Aug 18 03:19:43 EDT 2017

STATUS

proposed

approved

#22 by Emeric Deutsch at Fri Aug 18 01:52:12 EDT 2017

STATUS

editing

proposed