A374355 - OEIS

A374355

a(n) is the least 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, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 1, 4, 4, 4, 5, 0, 0, 0, 1, 0, 0, 2, 2, 8, 8, 8, 9, 8, 8, 10, 10, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 1, 4, 4, 4, 5, 16, 16, 16, 17, 16, 16, 18, 18, 16, 16, 16, 17, 20, 20, 20, 21, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 1, 4, 4, 4, 5, 0

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OFFSET

0,7

COMMENTS

To compute a(n): replace every other bit with zero (starting with the first 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, 0).

a(n) = n - A374356(n).

a(n) >= 0 with equality iff n is a fibbinary number.

EXAMPLE

The first terms, in binary and in decimal, are:

n a(n) bin(n) bin(a(n))

-- ---- ------ ---------

0 0 0 0

1 0 1 0

2 0 10 0

3 1 11 1

4 0 100 0

5 0 101 0

6 2 110 10

7 2 111 10

8 0 1000 0

9 0 1001 0

10 0 1010 0

11 1 1011 1

12 4 1100 100

13 4 1101 100

14 4 1110 100

15 5 1111 101

16 0 10000 0

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 += y; break; ); ); ); return (v); }

CROSSREFS

Cf. A003714, A374354, A374356.

Sequence in context: A035395 A116856 A140344 * A279479 A343630 A318584

Adjacent sequences: A374352 A374353 A374354 * A374356 A374357 A374358

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Jul 06 2024

STATUS

approved