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a(n) = least k>0 such that n^n divides Fibonacci(k).
3

%I #15 Jan 30 2014 11:02:32

%S 1,6,36,192,3125,3888,941192,12582912,516560652,7500000000,

%T 259374246010,743008370688,163086595857367,1190572159881216,

%U 583858520507812500,13835058055282163712,437950726881001816329,3278867339608044797952,1874292305362402347591138,78643200000000000000000000,2225747435575612389097571208

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

%H Max Alekseyev, <a href="/A215453/b215453.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A001177(n^n)

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

%o (Python)

%o TOP = 9

%o prpr = 0

%o prev = k = y = 1

%o res = [-1]*TOP

%o ii = [0]*TOP

%o for i in range(1, TOP):

%o ii[i] = i**i

%o while y<TOP:

%o for i in range(y, TOP):

%o if res[i]<0 and prev % ii[i] == 0:

%o res[i] = k

%o y += 1

%o for i in range(1, TOP):

%o print res[i],

%o print

%o curr = prpr+prev

%o prpr = prev

%o prev = curr

%o k += 1

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

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

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

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

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

%K nonn

%O 1,2

%A _Alex Ratushnyak_, Aug 11 2012

%E a(9) from _Giovanni Resta_, Jul 20 2013

%E Terms a(10) onward from _Max Alekseyev_, Jan 30 2014