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

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

Offset

1,1

Comments

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).

Links

Table of n, a(n) for n=1..10.

Example

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

Mathematica

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]

Crossrefs

Cf. A124202, A126283, A281889, A284411.

Sequence in context: A138787 A110052 A300626 * A039627 A231497 A309473

Adjacent sequences: A126279 A126280 A126281 * A126283 A126284 A126285

Keyword

nonn,more

Author

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

Status

approved