A126283 Largest number k for which the n-th prime is the median of the largest prime dividing the first k integers.

4, 18, 40, 76, 116, 182, 246, 330, 426, 532, 652, 770, 904, 1058, 1210, 1386, 1560, 1752, 1956, 2162, 2394, 2640, 2894, 3150, 3422, 3680, 3984, 4302, 4628, 4974, 5294, 5650, 5914, 6006, 6372, 6746, 7146, 7536, 7938, 8386, 8794, 9222, 9702, 10156

Offset: 1

Author

Mark Thornquist (mthornqu(AT)fhcrc.org) & Robert G. Wilson v, Dec 15 2006

Keywords

• nonn

Comments

a(14) = 1058 is the first term where a(n) exceeds A290154(n). - Peter Munn, Aug 02 2019

Examples

			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.
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}.
		

Crossrefs

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

Cf. A000040, A309366.

Programs

Mathematica

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