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A220463
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Chebyshev numbers C_v(n) for v=1.2: a(n) is the smallest number such that if x>=a(n), then theta(x)-theta(5*x/6)>=n*log(x), where theta(x)=sum_{prime p<=x}log p.
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2
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59, 137, 139, 149, 223, 241, 347, 353, 383, 389, 563, 569, 593, 613, 631, 641, 821, 823, 853, 929, 937, 1009, 1013, 1061, 1069, 1277, 1279, 1361, 1427, 1433, 1481, 1487, 1597, 1601, 1607, 1609, 1613, 1973, 1979, 1997, 2011, 2081, 2083, 2113, 2203, 2269, 2273, 2297
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OFFSET
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1,1
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COMMENTS
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All terms are primes.
Up to a(98)=5381, all terms are 1.2-Ramanujan numbers as in Shevelev's link; up to 5381, the only missing 1.2-Ramanujan numbers are 29 and 5171.
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LINKS
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N. Amersi, O. Beckwith, S. J. Miller, R. Ronan, J. Sondow, Generalized Ramanujan primes, Combinatorial and Additive Number Theory, Springer Proc. in Math. & Stat., CANT 2011 and 2012, Vol. 101 (2014), 1-13
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FORMULA
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a(n)<=prime(11*(n+1)).
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MATHEMATICA
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k=5; xs=Table[{m, Ceiling[x/.FindRoot[(x (-1300+Log[x]^4))/Log[x]^5==(k+1) m, {x, f[(k+1) m]-1}, AccuracyGoal->Infinity, PrecisionGoal->20, WorkingPrecision->100]]}, {m, 1, 101}]; Table[{m, 1+NestWhile[#-1&, xs[[m]][[2]], (1/Log[#1]Plus@@Log[Select[Range[Floor[(k #1)/(k+1)]+1, #1], PrimeQ]]&)[#]>m&]}, {m, 1, 100}] (* Peter J. C. Moses, Dec 20 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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