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Arrange copies of the n digits 1, ..., n such that there is one digit between the 1s, two digits between the 2s, etc. For example, the unique (modulo reversal) n=3 solution is 231213, and the unique (again modulo reversal) n=4 solution is 23421314.
- Visu August 12, 2015Solutions to Langford's problem exist only if n=0,3 (mod 4), so the next solutions occur for n=7.
There are 26 of these, as exhibited by Lloyd (1971).
In lexicographically smallest order (i.e., small digits come first), the first few Langford sequences are 231213, 23421314, 14156742352637, 14167345236275, 15146735423627, ...