A374356 a(n) is the greatest fibbinary number f <= n such that n - f is also a fibbinary number whose binary expansion has no common 1's with that of f (where fibbinary numbers correspond to A003714).

0, 1, 2, 2, 4, 5, 4, 5, 8, 9, 10, 10, 8, 9, 10, 10, 16, 17, 18, 18, 20, 21, 20, 21, 16, 17, 18, 18, 20, 21, 20, 21, 32, 33, 34, 34, 36, 37, 36, 37, 40, 41, 42, 42, 40, 41, 42, 42, 32, 33, 34, 34, 36, 37, 36, 37, 40, 41, 42, 42, 40, 41, 42, 42, 64, 65, 66, 66

Offset

0,3

Comments

To compute a(n): replace every other bit with zero (starting with the second bit) in each run of consecutive 1's in the binary expansion of n.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Index entries for sequences related to binary expansion of n

Formula

a(n) = A374354(n, A277561(n)-1).

a(n) = n - A374355(n).

a(n) <= n with equality iff n is a fibbinary number.

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     2      11         10
   4     4     100        100
   5     5     101        101
   6     4     110        100
   7     5     111        101
   8     8    1000       1000
   9     9    1001       1001
  10    10    1010       1010
  11    10    1011       1010
  12     8    1100       1000
  13     9    1101       1001
  14    10    1110       1010
  15    10    1111       1010
  16    16   10000      10000

Prog

(PARI) a(n) = { my (v = 0, e, x, y, b); while (n, x = y = 0; e = valuation(n, 2); for (k = 0, oo, if (bittest(n, e+k), n -= b = 2^(e+k); [x, y] = [y + b, x], v += x; break; ); ); ); return (v); }

Crossrefs

Cf. A003714, A277561, A374354, A374355.

Sequence in context: A292271 A292593 A332995 * A214793 A199088 A293974

Adjacent sequences: A374353 A374354 A374355 * A374357 A374358 A374359

Keyword

nonn,base

Author

Rémy Sigrist, Jul 06 2024

Status

approved