A215453 a(n) = least k>0 such that n^n divides Fibonacci(k).

1, 6, 36, 192, 3125, 3888, 941192, 12582912, 516560652, 7500000000, 259374246010, 743008370688, 163086595857367, 1190572159881216, 583858520507812500, 13835058055282163712, 437950726881001816329, 3278867339608044797952, 1874292305362402347591138, 78643200000000000000000000, 2225747435575612389097571208

Offset: 1

Author

Alex Ratushnyak, Aug 11 2012

Keywords

• nonn

Examples

			a(2): least k>0 such that 2^2 divides Fibonacci(k) is k=6: Fibonacci(6)=8. So a(2)=6.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001177 (least k such that n divides Fibonacci(k)).

Cf. A132632 (least k such that n^2 divides Fibonacci(k)).

Cf. A132633 (least k such that n^3 divides Fibonacci(k)).

Cf. A214528 (least k such that n! divides Fibonacci(k)).

Cf. A215011 (least k such that triangular(n) divides Fibonacci(k)).

Programs

Python

TOP = 9
prpr = 0
prev = k = y = 1
res = [-1]*TOP
ii = [0]*TOP
for i in range(1, TOP):
    ii[i] = i**i
while y
				

Formula

a(n) = A001177(n^n)

Extensions

a(9) from Giovanni Resta, Jul 20 2013

Terms a(10) onward from Max Alekseyev, Jan 30 2014