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A370744
a(n) is the greatest Fibonacci number f such that f AND n = f (where AND denotes the bitwise AND operator).
2
0, 1, 2, 3, 0, 5, 2, 5, 8, 8, 8, 8, 8, 13, 8, 13, 0, 1, 2, 3, 0, 21, 2, 21, 8, 8, 8, 8, 8, 21, 8, 21, 0, 1, 34, 34, 0, 5, 34, 34, 8, 8, 34, 34, 8, 13, 34, 34, 0, 1, 34, 34, 0, 21, 34, 55, 8, 8, 34, 34, 8, 21, 34, 55, 0, 1, 2, 3, 0, 5, 2, 5, 8, 8, 8, 8, 8, 13
OFFSET
0,3
COMMENTS
From Robert Israel, Mar 01 2024: (Start)
a(n) is the greatest Fibonacci number f <= n such that there are no carries in the base-2 addition of f and n-f.
a(n) is the greatest Fibonacci number f such that binomial(n, f) is odd. (End)
LINKS
FORMULA
a(n) <= n with equality iff n is a Fibonacci number.
MAPLE
Fib:= [seq(combinat:-fibonacci(n), n=0..100)]:
f:= proc(n) local m, k;
m:= ListTools:-BinaryPlace(Fib, n+1);
for k from m by -1 do
if MmaTranslator:-Mma:-BitAnd(Fib[k], n) = Fib[k] then return Fib[k] fi
od
end proc:
map(f, [$0..100]); # Robert Israel, Mar 01 2024
PROG
(PARI) a(n) = { my (v = 0, f); for (k = 2, oo, f = fibonacci(k); if (f > n, return (v), bitand(f, n)==f, v = f); ); }
CROSSREFS
Sequence in context: A272591 A339694 A074722 * A331102 A080368 A057174
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 29 2024
STATUS
approved