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单词 GolombsSequence
释义

Golomb’s sequence


Golomb’s sequenceMathworldPlanetmath is a self-referential ascending order sequence of integers a in which the number of times each number n occurrs is given by an. The sequence begins 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, … (see A001462 in Sloane’s OEIS). For example, a3=2 and indeed 3 occurs twice in the sequence. a4=3, so 4 occurs thrice.

The recurrence relationMathworldPlanetmath for the sequence is a1=1 and an=an-aaan-1+1. Sometimes recurrence relations for this sequence are given which also explicitly set a2=2. The nth term of the sequence can be obtained by the calculating ϕ2-ϕnϕ-1 (with

ϕ=1+52

being the golden ratioMathworldPlanetmath) and rounding off to the nearest integer. For example, with precision to five decimal places: 1.20178, 1.84448, 2.36975, 2.83087, 3.24948, 3.63706, 4.0006, 4.34477, 4.67284, 4.98724, 5.28984, 5.58209, 5.86518, 6.14005, 6.40753, 6.66827, 6.92286, 7.17178, 7.41548, etc.

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更新时间:2025/5/4 3:52:59