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A274695 a(1) = 1; for n>1, a(n) = smallest number > a(n-1) such that a(1)*a(2)*...*a(n) + 1 is a Fibonacci number. 0
1, 2, 6, 133, 97479304649455554938377 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(6) = (Fibonacci(7937)-1)/(a(2)*a(3)*a(4)*a(5)) has 1633 digits and it is thus too large to be included in Data section or in a b-file. - Giovanni Resta, Jul 05 2016

LINKS

Table of n, a(n) for n=1..5.

EXAMPLE

After a(1)=1 and a(2)=2, we want m, the smallest number > 2 such that 1*2*m+1 is a Fibonacci number: this is m = 6 = a(3).

MATHEMATICA

a[1] = 1; a[n_] := a[n] = Block[{p = Times @@ Array[a, n-1], i, m}, For[i=2, ! (IntegerQ[m = (Fibonacci[i] - 1)/p] && m > a[n-1]), i++]; m]; Array[a, 6] (* Giovanni Resta, Jul 05 2016 *)

PROG

(Sage)

product = 1

seq = [ product ]

prev_fib_index = 0

max_n = 5

for n in xrange(2, max_n+1):

    fib_index = prev_fib_index + 1

    found = False

    while not found:

        fib_minus_1 = fibonacci(fib_index) - 1

        if product.divides(fib_minus_1):

            m = int( fib_minus_1 / product )

            if m > seq[-1]:

                product = product * m

                seq.append( m )

                found = True

                prev_fib_index = fib_index

                break

        fib_index += 1

print seq

CROSSREFS

Cf. A000045, A046966.

Sequence in context: A181316 A101753 A288185 * A156515 A254223 A206849

Adjacent sequences:  A274692 A274693 A274694 * A274696 A274697 A274698

KEYWORD

nonn

AUTHOR

Robert C. Lyons, Jul 04 2016

EXTENSIONS

a(5) from Giovanni Resta, Jul 05 2016

STATUS

approved

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Last modified October 20 05:42 EDT 2017. Contains 293601 sequences.