A323213 Nearest prime to the median of the primes below 10^n.

5, 41, 439, 4523, 46411, 470303, 4751053, 47868179, 481346903, 4834216447, 48507378197, 486425324491, 4875521711327, 48850585043591, 489323461383733, 4900321995437591, 49065251868835099, 491200019422325489, 4916868348839249987, 49212253916770634411

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Kim Walisch, primecount.

Formula

a(n) = prime(floor(A006880(n) / 2) + 1). - David A. Corneth, Mar 19 2019

Example

From David A. Corneth, Mar 19 2019: (Start)
There are 25 primes <= 10^2 = 100 so a(2) is the (25 + 1)/2 = 13th prime, being 41.
There are 168 primes <= 10^3 = 1000 so a(3) is the prime closest to the average of prime(84) = 433 and prime(85) = 439. That average is 436, equally distant from both primes. So the largest is chosen. This disables the need to compute the median and we can immediately say that a(3) = prime(168 / 2 + 1) = 439. (End)

Mathematica

a[n_] := Prime[Floor[PrimePi[10^n]/2] + 1]; Array[a, 10] (* Amiram Eldar, Mar 20 2019 *)

Prog

(Julia) using Statistics, Primes
function MedianPrimes(n)
    med = Int64(round(median(primes(10^n))))
    isprime(med) && return med
    prevmed = prevprime(med); nextmed = nextprime(med)
    abs(med - prevmed) < abs(med - nextmed) ? prevmed : nextmed end
println([MedianPrimes(n) for n in 1:12])
(PARI) a(n) = pi = primepi(10^n); prime(pi \ 2 + 1) \\ David A. Corneth, Mar 19 2019

Crossrefs

Cf. A000040, A000720, A006880.

Sequence in context: A218219 A140095 A259609 * A083073 A115257 A225095

Adjacent sequences: A323210 A323211 A323212 * A323214 A323215 A323216

Keyword

nonn,more

Author

Peter Luschny, Mar 19 2019

Extensions

a(11) from David A. Corneth, Mar 19 2019

a(12)-a(19) using Kim Walisch's primecount, from Amiram Eldar, Mar 20 2019

a(20) from Jinyuan Wang, Nov 14 2020

Status

approved