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A334591 Side length of largest triangle of zeros in the XOR-triangle with first row generated from the binary expansion of n. 9
0, 1, 1, 2, 1, 1, 2, 3, 2, 2, 1, 2, 1, 2, 3, 4, 3, 2, 2, 2, 3, 1, 2, 3, 2, 2, 1, 2, 2, 3, 4, 5, 4, 3, 3, 2, 2, 3, 2, 3, 2, 4, 3, 2, 1, 2, 3, 4, 3, 2, 3, 2, 3, 1, 2, 3, 2, 2, 2, 3, 3, 4, 5, 6, 5, 4, 4, 3, 3, 3, 3, 3, 2, 3, 2, 4, 3, 2, 3, 4, 3, 2, 2, 4, 5, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

An XOR-triangle is an inverted 0-1 triangle formed by choosing a top row and having each entry in the subsequent rows be the XOR of the two values above it.

Records occur at a(2^n) = n.

Ones occur at 2, 3, 5, 6, 11, 13, 22, 27, 45, 54, 91, 109, 182, 219, 365, 438, 731, 877, 1462,...

a(n) <= A087117(n).

LINKS

Peter Kagey, Table of n, a(n) for n = 1..8191

MathOverflow user DSM, Number triangle

Index entries for sequences related to binary expansion of n

EXAMPLE

For n = 53, a(53) = 3 because 53 = 110101_2 in binary, and the largest triangle of 0s in the corresponding XOR-triangle has size 3 (see third, fourth, and fifth rows):

  1 1 0 1 0 1

   0 1 1 1 1

    1 0 0 0

     1 0 0

      1 0

       1

MATHEMATICA

Array[Function[w, Max@ Flatten@ Array[If[# == 1, If[First@ # == 1, Nothing, Length@ #] & /@ Split@ w[[#]], If[First@ # == -1, Length@ #, Nothing] & /@ Split[w[[#]] - Most@ w[[# - 1]] ] ] &, Length@ w] /. -Infinity -> 0]@ NestWhileList[Map[BitXor @@ # &, Partition[#, 2, 1]] &, IntegerDigits[#, 2], Length@ # > 1 &] &, 105] (* Michael De Vlieger, May 08 2020 *)

CROSSREFS

Cf. A087117, A334556, A334592, A334593, A334594, A334595, A334596.

Sequence in context: A338198 A091598 A144021 * A177962 A246552 A161091

Adjacent sequences:  A334588 A334589 A334590 * A334592 A334593 A334594

KEYWORD

nonn,base

AUTHOR

Peter Kagey, May 07 2020

STATUS

approved

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Last modified May 20 08:18 EDT 2022. Contains 353852 sequences. (Running on oeis4.)