亂數斐波那契數列是一個類似斐波那契數列的數列,由以下的遞迴關係式所定義:

fn = fn−1 ± fn−2

其中正負號是依亂數決定,概率各是1/2,每次的正負號有統計獨立性

依照Harry Kesten及Hillel Fürstenberg的理論,這類的亂數遞迴關係式會依某種指數增長的方式增長,但其增長的速率很難具體的計算出來,1999年時Divakar Viswanath證明亂數斐波那契數列的增長速率為1.1319882487943…(OEIS數列A078416),此常數後來也被命名為Viswanath常數。

參考資料

  • Viswanath, Divakar, Random Fibonacci sequences and the number 1.13198824…, Mathematics of Computation, 1999, 69 (231): 1131–1155, doi:10.1090/S0025-5718-99-01145-X.
  • Oliveira, J.B.; de Figueiredo, L.H., Interval computation of Viswanath's constant, Reliable Computing, 2002, 8 (2): 131–138., doi:10.1023/A:1014702122205

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