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米安-邱拉數列

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米安-邱拉数列(Mian-Chowla sequence)是以递归方式定義的整數數列,其首項為

而對於是對於所有不大於,以下的二項和

均不重複的最小整數。

性質

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第一項為,其二項和只有一個1 + 1 = 2,數列的下一項是,其二項和有2, 3, 4,都不重複。第三項不能是3,因為若是3,就會有重複的二項和1 + 3 = 2 + 2 = 4,可得到,二項和為2, 3, 4, 5, 6, 8。米安-邱拉数列的前幾項是

1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97, 123, 148, 182, 204, 252, 290, 361, 401, 475, ... (OEIS數列A005282).

類似數列

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若定義,所得的數列相近,不過每一項都比米安-邱拉数列要少1(0, 1, 3, 7, 12, 20, 30, 44, 65, 80, 96, ... A025582)。

歷史

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此數列是由阿布杜爾·馬基德·米安和薩爾瓦達曼·邱拉英语Sarvadaman Chowla所發現。

參考資料

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  • S. R. Finch, Mathematical Constants, Cambridge (2003): Section 2.20.2
  • R. K. Guy Unsolved Problems in Number Theory, New York: Springer (2003)
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米安-邱拉數列
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