OFFSET
1,1
REFERENCES
S. Ramanujan, Collected Papers of Srinivasa Ramanujan (Ed. G. H. Hardy, S. Aiyar, P. Venkatesvara and B. M. Wilson), Amer. Math. Soc., Providence, 2000, pp. 208-209.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
S. Ramanujan, A proof of Bertrand's postulate, J. Indian Math. Soc., 11 (1919), 181-182.
V. Shevelev, Ramanujan and Labos primes, their generalizations and classifications of primes, arXiv:0909.0715 [math.NT], 2009-2011.
J. Sondow, Ramanujan Prime in MathWorld
J. Sondow and E. W. Weisstein, Bertrand's Postulate in MathWorld
J. Sondow, Ramanujan primes and Bertrand's postulate, Amer. Math. Monthly, 116 (2009), 630-635; arXiv:0907.5232 [math.NT], 2009-2010.
Wikipedia, Ramanujan prime
FORMULA
a(n) = Max{x; Pi[x]-Pi[x/2]=n} = Max{x; A056171(x)=n} = Max{x; A056169(n!)=n}; where Pi()=A000720().
a(n) = A104272(n+1) - 1. [Jonathan Sondow, Aug 11 2008]
EXAMPLE
n=5: in 46! five unitary-prime-divisors[UPD] appear: {29,31,37,41,43}. In larger factorials number of UPD is not more equal 5. Thus a(5)=46.
MATHEMATICA
nn = 60; R = Table[0, {nn}]; s = 0;
Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < nn, R[[s+1]] = k], {k, Prime[3*nn]}];
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Feb 21 2003
EXTENSIONS
Definition corrected by Jonathan Sondow, Aug 10 2008
STATUS
approved