A089961 a(n) = floor( 1/( {n/phi}-{n/phi}^2 ) )-1, where {} is the fractional part and phi the golden ratio.

3, 4, 7, 3, 11, 3, 3, 18, 3, 5, 5, 3, 29, 3, 4, 9, 3, 8, 4, 3, 47, 3, 4, 6, 3, 14, 3, 3, 13, 3, 6, 4, 3, 76, 3, 4, 7, 3, 9, 3, 3, 23, 3, 5, 5, 3, 21, 3, 3, 10, 3, 7, 4, 3, 123, 3, 4, 6, 3, 12, 3, 3, 15, 3, 6, 5, 3, 38, 3

Offset

1,1

Comments

a(Fibonacci(n)) = Lucas(n), n>=2, where Fibonacci=A000045 and Lucas=A000032.

a(Lucas(n)) = Fibonacci(n), n>=4.

Examples: a(8) = 18, where 8 = Fibonacci(6) and 18 = Lucas(6). a(29) = 13, where 29 = Lucas(7) and 13 = Fibonacci(7).

Links

Table of n, a(n) for n=1..69.

Formula

a(n) = A089959(n) - 1.

Maple

fpart := proc(x)
        x-floor(x) ;
end proc:
A089961 := proc(n)
    invphi := 2/(1+sqrt(5)) ;
    fn := fpart(n*invphi) ;
    1/fn/(1-fn);
    floor(%)-1 ;
end proc: # R. J. Mathar, May 11 2013

Crossrefs

Cf. A001622, A089959.

Sequence in context: A130880 A026248 A082089 * A359954 A316498 A200681

Adjacent sequences: A089958 A089959 A089960 * A089962 A089963 A089964

Keyword

nonn

Author

Gary W. Adamson, Nov 20 2003

Status

approved