A343271 From left to right: 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, 3, 4, 5, 7, 7, 8, 9, 10, 11, 14, 15, 15, 15, 16, 16, 18, 19, 20, 21, 23, 23, 28, 29, 31, 31, 31, 31, 31, 31, 32, 32, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 46, 47, 47, 47, 56, 57, 58, 59, 62, 63, 63, 63, 62, 63, 63, 63, 63, 63, 63, 63, 64, 64, 64, 64

Offset

0,3

Comments

Leading zeros are ignored.

This sequence has similarities with A343049; here we scan the binary representations from left to right, there from right to left.

Links

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

Index entries for sequences related to binary expansion of n

Formula

A070939(a(n)) = 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     3      11         11
   4     4     100        100
   5     5     101        101
   6     7     110        111
   7     7     111        111
   8     8    1000       1000
   9     9    1001       1001
  10    10    1010       1010
  11    11    1011       1011
  12    14    1100       1110
  13    15    1101       1111
  14    15    1110       1111
  15    15    1111       1111

Prog

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

Crossrefs

Cf. A070939, A343049.

Sequence in context: A255545 A034152 A344316 * A363897 A114707 A000015

Adjacent sequences: A343268 A343269 A343270 * A343272 A343273 A343274

Keyword

nonn,base

Author

Rémy Sigrist, Apr 10 2021

Status

approved