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
Keywords
Links
- Hugo Pfoertner, Table of n, a(n) for n = 2..10000
Programs
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Mathematica
Table[Median@Select[Range[n^2,(n+1)^2],PrimeQ],{n,2,51}] (* Giorgos Kalogeropoulos, Dec 05 2021 *) -
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
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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
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