

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).


4



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
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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



FORMULA

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



KEYWORD

nonn,base


AUTHOR



STATUS

approved



