A276488 Numbers k that divide A003714(k).

1, 2, 8, 84, 130, 288, 856, 1034, 1230, 2568, 11200, 36565, 41509, 81536, 212586, 409541, 516368, 521248, 984064, 1771007, 5835276, 6230310, 11951289, 12298144, 16284017, 32568034, 32655554, 39382944, 69585548, 69656573, 101118154, 309345058, 384373140, 1165237916, 2623448060

Offset

1,2

Comments

Corresponding Fibbinary numbers are 1, 2, 16, 336, 650, 2304, 10272, ...

Next term > 2^32. - Joerg Arndt, Sep 05 2016

Links

Table of n, a(n) for n=1..35.

Example

84 = Fibonacci(10) + Fibonacci(8) + Fibonacci(6) and 84 divides A003714(84) = 2^8 + 2^6 + 2^4 = 336.

Prog

(C++)
#include <iostream>
typedef unsigned long ulong;
ulong next_fibrep(ulong x)
{
    ulong y = x | (x>>1);
    ulong z = y + 1;
    z = z & -z;
    x ^= z;
    x &= ~(z-1);
    return x;
}
int main()
{
    ulong n = 0;
    ulong f = 0;
    do
    {
        n += 1;
        f = next_fibrep(f);
        if ( f % n == 0 )
        {
            std::cout << n << ", ";
            std::cout << std::flush;
        }
    }
    while ( n <= (1UL << 32) );
    std::cout << std::endl;
} // Joerg Arndt, Sep 05 2016

Crossrefs

Cf. A003714, A357073.

Sequence in context: A120820 A295600 A336252 * A295764 A261683 A134089

Adjacent sequences: A276485 A276486 A276487 * A276489 A276490 A276491

Keyword

nonn

Author

Altug Alkan, Sep 05 2016

Extensions

Terms 2568 and beyond from Joerg Arndt, Sep 05 2016

Status

approved