A054495 Smallest k such that n/k is a Fibonacci number.

1, 1, 1, 2, 1, 2, 7, 1, 3, 2, 11, 4, 1, 7, 3, 2, 17, 6, 19, 4, 1, 11, 23, 3, 5, 2, 9, 14, 29, 6, 31, 4, 11, 1, 7, 12, 37, 19, 3, 5, 41, 2, 43, 22, 9, 23, 47, 6, 49, 10, 17, 4, 53, 18, 1, 7, 19, 29, 59, 12, 61, 31, 3, 8, 5, 22, 67, 2, 23, 14, 71, 9, 73, 37, 15, 38, 77, 6, 79, 10, 27, 41

Offset

1,4

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = n/A054494(n). [Corrected by Charles R Greathouse IV, Nov 05 2014]

Example

a(10)=2 because 10/1=10 is not a Fibonacci number but 10/2=5 is.

Prog

(PARI) A010056(n)=my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8))
a(n)=fordiv(n, d, if(A010056(n/d), return(d))) \\ Charles R Greathouse IV, Nov 05 2014
(Python)
from sympy import divisors
from sympy.ntheory.primetest import is_square
def A054495(n): return next(d for d in divisors(n) if is_square(m:=5*(n//d)**2-4) or is_square(m+8)) # Chai Wah Wu, May 06 2024

Crossrefs

Cf. A000045, A010056, A005086, A037943.

Sequence in context: A212671 A131057 A051852 * A007966 A224609 A278710

Adjacent sequences: A054492 A054493 A054494 * A054496 A054497 A054498

Keyword

easy,nonn,changed

Author

Henry Bottomley, Apr 04 2000

Extensions

a(34), a(55), a(68) corrected by Charles R Greathouse IV, Nov 06 2014

Status

approved