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Largest number k for which the n-th prime is the median of the largest prime dividing the first k integers.
4

%I #11 Feb 07 2020 21:09:02

%S 4,18,40,76,116,182,246,330,426,532,652,770,904,1058,1210,1386,1560,

%T 1752,1956,2162,2394,2640,2894,3150,3422,3680,3984,4302,4628,4974,

%U 5294,5650,5914,6006,6372,6746,7146,7536,7938,8386,8794,9222,9702,10156

%N Largest number k for which the n-th prime is the median of the largest prime dividing the first k integers.

%C a(14) = 1058 is the first term where a(n) exceeds A290154(n). - _Peter Munn_, Aug 02 2019

%e a(1)=4 because the median of {2,3,2} = {2, *2*,3} is 2 (the * surrounds the median) and for any number greater than 4 the median is greater than 2.

%e a(1)=18 because the median of {2,3,2,5,3,7,2,3,5,11,3,13,7,5,2,17,3} = {2,2,2,2,3,3,3,3, *3*,5,5,5,7,7,11,13,17}.

%t t = Table[0, {100}]; lst = {}; Do[lpf = FactorInteger[n][[ -1, 1]]; AppendTo[lst, lpf]; mdn = Median@lst; If[PrimeQ@ mdn, t[[PrimePi@mdn]] = n], {n, 2, 10^4}]; t

%Y Other sequences about medians of prime factors: A124202, A126282, A281889, A284411, A290154, A308904.

%Y Cf. A000040, A309366.

%K nonn

%O 1,1

%A Mark Thornquist (mthornqu(AT)fhcrc.org) & _Robert G. Wilson v_, Dec 15 2006