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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A188672 a(n) is the least r > 1 for which the interval (r*n, r*(n+1)) contains no prime powers (p^k, k >= 1), or a(n) = 0 if no such r exists.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 3, 0, 0, 0, 6, 2, 2, 3, 2, 7, 4, 2, 4, 0, 2, 7, 2, 2, 4, 3, 2, 2, 4, 2, 4, 4, 2, 2, 3, 5, 5, 2, 2, 3, 2, 2, 2, 3, 2, 4, 3, 2, 3, 4, 2, 0, 2, 2, 2, 5, 2, 3, 4, 2, 5, 2, 2, 3, 3, 2, 2, 2, 2, 4, 4, 2, 2, 3, 2, 2, 3, 2, 4, 3, 2, 3, 2
Offset: 1

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Author

Vladimir Shevelev and Peter J. C. Moses, Aug 26 2013

Keywords

Comments

Conjecture: a(n) = 0, iff n = 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 24, 56.
A proof that the interval(r*n, r*(n+1)) for r > 1 always contains a term from A000961 for n = 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 24, 56 uses methods based on the corresponding analog of Ramanujan numbers (cf. A228592) and their generalization.

Crossrefs

Cf. A000961, A218831, A228518, A228592.

Formula

If a(n)*A228518(n) is not 0, then a(n) >= A228518(n).
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