A349791 a(n) is the median of the primes between n^2 and (n+1)^2.

6, 12, 19, 30, 42, 59, 72, 89, 107, 134, 157, 181, 205, 236, 271, 311, 348, 381, 421, 461, 503, 560, 601, 650, 701, 754, 821, 870, 933, 994, 1051, 1113, 1193, 1268, 1319, 1423, 1482, 1559, 1624, 1723, 1801, 1884, 1993, 2081, 2148, 2267, 2357, 2444, 2549, 2663

Offset

2,1

Comments

The median of an even number of values is assumed to be defined as the arithmetic mean of the two central elements in their sorted list. The special case of the primes 2 and 3 in the interval [1,4] is excluded because their median would be 5/2.

Links

Hugo Pfoertner, Table of n, a(n) for n = 2..10000

Mathematica

Table[Median@Select[Range[n^2, (n+1)^2], PrimeQ], {n, 2, 51}] (* Giorgos Kalogeropoulos, Dec 05 2021 *)

Prog

(PARI) medpsq(n) = {my(p1=nextprime(n^2), p2=precprime((n+1)^2), np1=primepi(p1), np2=primepi(p2), nm=(np1+np2)/2);
if(denominator(nm)==1, prime(nm), (prime(nm-1/2)+prime(nm+1/2))/2)};
for(k=2, 51, print1(medpsq(k), ", "))
(Python)
from sympy import primerange
from statistics import median
def a(n): return int(median(primerange(n**2, (n+1)**2)))
print([a(n) for n in range(2, 52)]) # Michael S. Branicky, Dec 05 2021
(Python)
from sympy import primepi, prime
def A349791(n):
    b = primepi(n**2)+primepi((n+1)**2)+1
    return (prime(b//2)+prime((b+1)//2))//2 if b % 2 else prime(b//2) # Chai Wah Wu, Dec 05 2021

Crossrefs

Cf. A000290, A000720, A014085, A309359, A349792.

Sequence in context: A365702 A215342 A146923 * A256977 A087883 A218438

Adjacent sequences: A349788 A349789 A349790 * A349792 A349793 A349794

Keyword

nonn

Author

Hugo Pfoertner, Dec 05 2021

Status

approved