A342126 The binary expansion of a(n) corresponds to that of n where all the 1's have been replaced by 0's except in the first run of 1's.

0, 1, 2, 3, 4, 4, 6, 7, 8, 8, 8, 8, 12, 12, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 24, 24, 24, 24, 28, 28, 30, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 48, 48, 48, 48, 48, 48, 48, 48, 56, 56, 56, 56, 60, 60, 62, 63, 64, 64, 64, 64

Offset

0,3

Comments

In other words, this sequence gives the first run of 1's in the binary expansion of a number.

A023758(n) appears A057728(n) times.

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) = n - A087734(n).

a(2*n) = 2*a(n).

a(a(n)) = a(n).

a(n) <= n with equality iff n belongs to A023758.

Example

The first terms, alongside their binary expansion, 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     4     101        100
   6     6     110        110
   7     7     111        111
   8     8    1000       1000
   9     8    1001       1000
  10     8    1010       1000
  11     8    1011       1000
  12    12    1100       1100
  13    12    1101       1100
  14    14    1110       1110
  15    15    1111       1111

Prog

(PARI) a(n) = { my (b=binary(n), p=1); for (k=1, #b, b[k] = p*=b[k]); fromdigits(b, 2) }
(Python)
def A342126(n):
    s = bin(n)[2:]
    i = s.find('0')
    return n if i == -1 else (2**i-1)*2**(len(s)-i) # Chai Wah Wu, Apr 29 2021

Crossrefs

Cf. A023758, A057728, A087734, A090996, A342410.

Sequence in context: A076332 A370681 A245092 * A092601 A353705 A162906

Adjacent sequences: A342123 A342124 A342125 * A342127 A342128 A342129

Keyword

nonn,base,easy

Author

Rémy Sigrist, Apr 25 2021

Status

approved