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 unique 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
a1 = 1
Therefore, 1 occurs exactly one time in this sequence.
a2 > 1
a2 = 2
2 occurs exactly 2 times in this sequence.
a3 = 2
3 occurs exactly 2 times in this sequence.
a4 = a5 = 3
4 occurs exactly 3 times in this sequence.
5 occurs exactly 3 times in this sequence.
a6 = a7 = a8 = 4
a9 = a10 = a11 = 5
where is the golden ratio (approximately equal to 1.618034).
- Everest, Graham; van der Poorten, Alf; Shparlinski, Igor; Ward, Thomas (2003). Recurrence sequences. Mathematical Surveys and Monographs. 104. Providence, RI: American Mathematical Society. pp. 10, 256. ISBN 0-8218-3387-1. Zbl 1033.11006.
- Guy, Richard K. (2004). Unsolved problems in number theory (3rd ed.). Springer-Verlag. Section E25. ISBN 0-387-20860-7. Zbl 1058.11001.