A228518 a(n) is the least r > 1 for which the interval (r*n, r*(n+1)) contains no terms of A050376 or a(n) = 0 if no such r exists.

0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 3, 0, 2, 0, 6, 2, 2, 3, 2, 7, 3, 2, 4, 0, 2, 7, 2, 2, 4, 3, 2, 2, 4, 2, 4, 4, 2, 2, 3, 5, 3, 2, 2, 3, 2, 2, 2, 3, 2, 4, 3, 2, 3, 4, 2, 0, 2, 2, 2, 5, 2, 2, 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

Author

Vladimir Shevelev and Peter J. C. Moses, Aug 24 2013

Keywords

• nonn

Comments

It is an a Fermi-Dirac analog of A218831, since terms of A050376 play a role of primes in Fermi-Dirac arithmetic (see comments in A050376).

Conjecture: a(n) = 0 iff n = 1, 2, 3, 4, 5, 6, 9, 12, 14, 24, 56.

A proof that the interval(r*n, r*(n+1)) for r > 1 always contains a term from A050376 for n = 1, 2, 3, 4, 5, 6, 9, 12, 14, 24, 56 uses similar methods of analog of Ramanujan numbers (cf. A228520) and their generalization.

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A218831, A228520, A188672.

Formula

If a(n)*A218831(n) is not 0, then a(n) >= A218831(n).

If a(n)*A188672(n) is not 0, then a(n) <= A188672(n).