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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
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 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
Sequence in context: A101753 A288185 A359961 * A156515 A254223 A206849
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 June 20 23:53 EDT 2024. Contains 373535 sequences. (Running on oeis4.)