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Search: id:A140894
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| A140894 |
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A triangle of p-adic Binet like numbers: t(n,m)=((( 1 + Sqrt[Prime[n]]))^m - (( 1 - Sqrt[Prime[n]]))^m)/(2*Sqrt[Prime[n]]). |
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1
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| 1, 1, 2, 1, 2, 8, 1, 2, 10, 32, 1, 2, 14, 48, 236, 1, 2, 16, 56, 304, 1280, 1, 2, 20, 72, 464, 2080, 11584, 1, 2, 22, 80, 556, 2552, 15112, 76160, 1, 2, 26, 96, 764, 3640, 24088, 128256, 786448, 1, 2, 32, 120, 1136, 5632, 43072, 243840, 1693696, 10214912
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums are:
{1, 3, 11, 45, 301, 1659, 14223, 94485, 943321, 12202443}.
The use of primes makes sure that these are sums of two irrational numbers
that are root solutions to quadratic polynomials.
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REFERENCES
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Weisstein, Eric W. "Binet's Fibonacci Number Formula." http://mathworld.wolfram.com/BinetsFibonacciNumberFormula.html
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FORMULA
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t(n,m)=((( 1 + Sqrt[Prime[n]]))^m - (( 1 - Sqrt[Prime[n]]))^m)/(2*Sqrt[Prime[n]]).
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EXAMPLE
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{1},
{1, 2},
{1, 2, 8},
{1, 2, 10, 32},
{1, 2, 14, 48, 236},
{1, 2, 16, 56, 304, 1280},
{1, 2, 20, 72, 464, 2080, 11584},
{1, 2, 22, 80, 556, 2552, 15112, 76160},
{1, 2, 26, 96, 764, 3640, 24088, 128256, 786448},
{1, 2, 32, 120, 1136, 5632, 43072, 243840, 1693696, 10214912}
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MATHEMATICA
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Binet[n_, m_] := (((1 + Sqrt[Prime[n]]))^m - (( 1 - Sqrt[Prime[n]]))^m)/(2*Sqrt[Prime[n]]); a = Table[Table[ExpandAll[Binet[n, m]], {m, 1, n}], {n, 1, 10}] Flatten[a]
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CROSSREFS
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Cf. A117809.
Sequence in context: A103410 A114303 A030651 this_sequence A137305 A143208 A119419
Adjacent sequences: A140891 A140892 A140893 this_sequence A140895 A140896 A140897
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jul 23 2008
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