A343049 The k-th binary digit of a(n) is the most frequent digit among the first k binary digits of n (in case of a tie, take the k-th binary digit of n).

0, 1, 2, 7, 0, 5, 6, 31, 0, 9, 10, 31, 8, 29, 30, 127, 0, 1, 2, 23, 0, 21, 22, 127, 0, 25, 26, 127, 24, 125, 126, 511, 0, 1, 2, 39, 0, 37, 38, 127, 0, 41, 42, 127, 40, 125, 126, 511, 0, 33, 34, 119, 32, 117, 118, 511, 32, 121, 122, 511, 120, 509, 510, 2047, 0

Offset

0,3

Comments

Leading zeros are taken into account up to the point the number of zeros exceeds the total number of ones.

We scan the binary representation of a number starting from the least significant digit. See A343271 for the other way.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

Formula

a(n) = 0 iff n belongs to A036993.

a(n) = n iff n = 0 or n belongs to A032925.

a(2^k-1) = 2^(2*k-1)-1 for any k > 1.

A070939(a(n)) < 2*A070939(n).

Example

The first terms, in decimal and in binary, are:
  n   a(n)  bin(n)  bin(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     1       1          1
   2     2      10         10
   3     7      11        111
   4     0     100          0
   5     5     101        101
   6     6     110        110
   7    31     111      11111
   8     0    1000          0
   9     9    1001       1001
  10    10    1010       1010
  11    31    1011      11111
  12     8    1100       1000
  13    29    1101      11101
  14    30    1110      11110
  15   127    1111    1111111

Prog

(PARI) a(n, base=2) = { my (d=digits(n, base), t, f=vector(base)); d=concat(vector(#d), d); forstep (k=#d, 1, -1, f[1+d[k]]++; if (vecmax(f)==f[1+d[k]], t=d[k]; ); d[k]=t); fromdigits(d, base) }

Crossrefs

Cf. A032925, A036993, A070939, A343271, A342697.

Sequence in context: A277815 A229178 A019667 * A098198 A021791 A325905

Adjacent sequences: A343046 A343047 A343048 * A343050 A343051 A343052

Keyword

nonn,base

Author

Rémy Sigrist, Apr 09 2021

Status

approved