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 a1 = 1, and with the property that for n > 1 each an is the smallest integer which makes it possible to satisfy the condition. For example, a1 = 1 says that 1 only occurs once in the sequence, so a2 cannot be 1 too, but it can be, and therefore must be, 2.

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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 a1 = 1, and with the property that for n > 1 each an is the smallest integer which makes it possible to satisfy the condition. For example, a1 = 1 says that 1 only occurs once in the sequence, so a2 cannot be 1 too, but it can be, and therefore must be, 2. The first few values are Colin Mallows has given an explicit recurrence relation a(1) = 1; a(n + 1) = 1 + a(n + 1 − a). An asymptotic expression for an is <math>\varphi^{2-\varphi}n^{\varphi-1},</math> where φ is the golden ratio.
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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 a1 = 1, and with the property that for n > 1 each an is the smallest integer which makes it possible to satisfy the condition. For example, a1 = 1 says that 1 only occurs once in the sequence, so a2 cannot be 1 too, but it can be, and therefore must be, 2.
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  • Golomb sequence
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