A Fibonacci-like Sequence of Composite Numbers
نویسنده
چکیده
In 1964, Ronald Graham proved that there exist relatively prime natural numbers a and b such that the sequence {An} defined by An = An−1 +An−2 (n ≥ 2;A0 = a,A1 = b) contains no prime numbers, and constructed a 34-digit pair satisfying this condition. In 1990, Donald Knuth found a 17-digit pair satisfying the same conditions. That same year, noting an improvement to Knuth’s computation, Herbert Wilf found a yet smaller 17-digit pair. Here we improve Graham’s construction and generalize Wilf’s note, and show that the 12-digit pair (a, b) = (407389224418, 76343678551) also defines such a sequence. Mathematical Reviews Subject Numbers: 11B39, 11N99.
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A New Kind of Fibonacci-Like Sequence of Composite Numbers
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عنوان ژورنال:
- Electr. J. Comb.
دوره 6 شماره
صفحات -
تاریخ انتشار 1999