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.

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

1,7

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.

Links

Table of n, a(n) for n=1..87.

Formula

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

Crossrefs

Cf. A000961, A218831, A228518, A228592.

Sequence in context: A045872 A154463 A011165 * A228518 A379115 A279647

Adjacent sequences: A188669 A188670 A188671 * A188673 A188674 A188675

Keyword

nonn

Author

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

Status

approved