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

1,2

Links

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

Formula

a(n) = A001177(n^n)

Example

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

Prog

(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<TOP:
    for i in range(y, TOP):
      if res[i]<0 and prev % ii[i] == 0:
        res[i] = k
        y += 1
        for i in range(1, TOP):
          print res[i],
        print
    curr = prpr+prev
    prpr = prev
    prev = curr
    k += 1

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)).

Sequence in context: A146883 A159721 A106539 * A267229 A048980 A200782

Adjacent sequences: A215450 A215451 A215452 * A215454 A215455 A215456

Keyword

nonn

Author

Alex Ratushnyak, Aug 11 2012

Extensions

a(9) from Giovanni Resta, Jul 20 2013

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

Status

approved