OFFSET
1,1
COMMENTS
All terms are primes==2 (mod 3).
For the definition of generalized Ramanujan numbers, see Section 6 of the Shevelev, Greathouse, & Moses link.
We conjecture that for all n >= 1, a(n) <= A104272(3*n). This conjecture is based on observation that, if interval (x/2, x] contains >= 3*n primes, then at least n of them are of the form 3*k+2.
LINKS
Vladimir Shevelev, Charles R. Greathouse IV, Peter J. C. Moses, On intervals (kn, (k+1)n) containing a prime for all n>1, Journal of Integer Sequences, Vol. 16 (2013), Article 13.7.3. arXiv:1212.2785
FORMULA
lim(a(n)/prime(4*n)) = 1 as n tends to infinity.
MATHEMATICA
Table[1 + NestWhile[#1 - 1 &, A104272[[3 k]], Count[Mod[Select[Range@@{Floor[#1/2 + 1], #1}, PrimeQ], 3], 2] >= k &], {k, 1, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev and Peter J. C. Moses, Dec 18 2012
STATUS
approved