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.

1, 2, 6, 133, 97479304649455554938377

Offset: 1

Author

Robert C. Lyons, Jul 04 2016

Keywords

• nonn

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

Examples

			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).
		

Crossrefs

Cf. A000045, A046966.

Programs

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 *)

Sage

product = 1
seq = [ product ]
prev_fib_index = 0
max_n = 5
for n in range(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)

Extensions

a(5) from Giovanni Resta, Jul 05 2016