A124202 -id:A124202 - cp's OEIS frontend

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

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

nonn

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

			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}.

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

Cf. A000040, A309366.

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

A126282 Median of the largest prime dividing the first 10^n numbers greater than 1.

Original entry on oeis.org

3, 11, 43, 191, 797, 3259, 13267, 54049, 219277, 887707

Offset: 1

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

A randomly selected number <= 10^n (uniform distribution from 2 to 10^n) has a 50% probability of having a prime factor at least as large as a(n).

			The largest prime divisors of the nonunit 1-digit numbers are 2, 3, 2, 5, 3, 7, 2 and 3 respectively, with median 3.

Cf. A124202, A126283, A281889, A284411.

f[n_Integer(* n must be even so as to find a true median, not an average, and n must be greater than *)] := Block[{cnt, lmt = n/2, p = PrimePi[n/2], q = PrimePi[n]}, cnt = q - p; p--; While[cnt < lmt, cnt = cnt + Floor[n/Prime@ p]; p-- ]; p++; Prime@ p]; MapAt[# + 1 &, Reap[Do[Sow@ f[10^n], {n, 6}]][[-1, -1]], 1]

cp's OEIS Frontend

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

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