A Lucas Triangle Primality Criterion Dual to That of Mann-shanks
نویسنده
چکیده
subject to the initial conditions A(l, 0) = 1, A(l, 1) ='2, with 4(n, /c) = 0 for & < 0 or k > n. This array has been called a Lucas triangle by Feinberg [1], because rising diagonals sum to give the Lucas numbers 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, ..., in contrast to the rising diagonals in the standard Pascal triangle where rising diagonals sum to give the Fibonacci numbers 1, 1, 2, 3, 5, 8, ... . The seventh diagonal in our array is 15 7, 14, 7; the eleventh diagonal is 1, 11, 44, 77, 55, 11. This suggests the following.
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