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

%I A215453 #19 Aug 04 2025 10:40:05
%S A215453 1,6,36,192,3125,3888,941192,12582912,516560652,7500000000,
%T A215453 259374246010,743008370688,163086595857367,1190572159881216,
%U A215453 583858520507812500,13835058055282163712,437950726881001816329,3278867339608044797952,1874292305362402347591138,78643200000000000000000000,2225747435575612389097571208
%N A215453 a(n) = least k>0 such that n^n divides Fibonacci(k).
%H A215453 Max Alekseyev, <a href="/A215453/b215453.txt">Table of n, a(n) for n = 1..1000</a>
%F A215453 a(n) = A001177(n^n)
%e A215453 a(2): least k>0 such that 2^2 divides Fibonacci(k) is k=6: Fibonacci(6)=8. So a(2)=6.
%o A215453 (Python)
%o A215453 TOP = 9
%o A215453 prpr = 0
%o A215453 prev = k = y = 1
%o A215453 res = [-1]*TOP
%o A215453 ii = [0]*TOP
%o A215453 for i in range(1, TOP):
%o A215453     ii[i] = i**i
%o A215453 while y<TOP:
%o A215453     for i in range(y, TOP):
%o A215453       if res[i]<0 and prev % ii[i] == 0:
%o A215453         res[i] = k
%o A215453         y += 1
%o A215453         print(res)
%o A215453     curr = prpr+prev
%o A215453     prpr = prev
%o A215453     prev = curr
%o A215453     k += 1
%Y A215453 Cf. A001177 (least k such that n divides Fibonacci(k)).
%Y A215453 Cf. A132632 (least k such that n^2 divides Fibonacci(k)).
%Y A215453 Cf. A132633 (least k such that n^3 divides Fibonacci(k)).
%Y A215453 Cf. A214528 (least k such that n! divides Fibonacci(k)).
%Y A215453 Cf. A215011 (least k such that triangular(n) divides Fibonacci(k)).
%K A215453 nonn
%O A215453 1,2
%A A215453 _Alex Ratushnyak_, Aug 11 2012
%E A215453 a(9) from _Giovanni Resta_, Jul 20 2013
%E A215453 Terms a(10) onward from _Max Alekseyev_, Jan 30 2014