A228518 - OEIS

%I #16 Aug 28 2013 22:23:22

%S 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,

%T 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,

%U 3,2,2,2,2,4,4,2,2,3,2,2,3,2,4,3,2,3,2

%N 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.

%C 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).

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

%C 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.

%H Peter J. C. Moses, <a href="/A228518/b228518.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%Y Cf. A218831, A228520, A188672.

%K nonn

%O 1,7

%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Aug 24 2013