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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 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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