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In mathematics, the Golomb sequence, named after Solomon W. Golomb (but also called Silverman's sequence), is a non-decreasing integer sequence where ''an'' is the number of times that ''n'' occurs in the sequence, starting with ''a''1 = 1, and with the property that for ''n'' > 1 each ''an'' is the unique integer which makes it possible to satisfy the condition. For example, ''a''1 = 1 says that 1 only occurs once in the sequence, so ''a''2 cannot be 1 too, but it can be, and therefore must be, 2. The first few values are :1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12 . ''a''1 = 1 Therefore, 1 occurs exactly one time in this sequence. ''a''2 > 1 ''a''2 = 2 2 occurs exactly 2 times in this sequence. ''a''3 = 2 3 occurs exactly 2 times in this sequence. ''a''4 = ''a''5 = 3 4 occurs exactly 3 times in this sequence. 5 occurs exactly 3 times in this sequence. ''a''6 = ''a''7 = ''a''8 = 4 ''a''9 = ''a''10 = ''a''11 = 5 etc. Colin Mallows has given an explicit recurrence relation . An asymptotic expression for ''an'' is : where ''φ'' is the golden ratio. ==References== * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Golomb sequence」の詳細全文を読む スポンサード リンク
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