

A274695


a(1) = 1; for n>1, a(n) = smallest number > a(n1) such that a(1)*a(2)*...*a(n) + 1 is a Fibonacci number.


0




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 bfile.  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, n1], i, m}, For[i=2, ! (IntegerQ[m = (Fibonacci[i]  1)/p] && m > a[n1]), 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 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)


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



