A378904 2*a(n) are the gaps that correspond to A350100(n).

1, 2, 3, 7, 9, 10, 12, 13, 15, 17, 18, 20, 26, 27, 29, 33, 39, 41, 66, 75, 84, 90, 95, 100, 113, 126, 140, 144, 155, 162, 177, 204, 206, 210, 216, 302, 303, 364, 389, 391, 399, 418, 441, 469, 492, 497, 504, 520, 613, 723

Offset: 1

Author

Hugo Pfoertner, Dec 15 2024

Keywords

• nonn
• more

Crossrefs

Cf. A058043, A350100.

Programs

PARI

a378904(kmax) = my(d=0); for(k=2, kmax, my(k2=k*k, dd=(nextprime(k2)-precprime(k2))/2); if(dd>d, print1(dd,", "); d=dd));
a378904(10^6)

Python

from itertools import count, islice
from sympy import prevprime, nextprime
def A378904_gen(): # generator of terms
    c = 0
    for k in count(2):
        a = nextprime(m:=k**2)-prevprime(m)
        if a>c:
            yield a>>1
            c = a
A378904_list = list(islice(A378904_gen(),20)) # Chai Wah Wu, Dec 17 2024

Extensions

a(50) from Hugo Pfoertner, Jan 04 2025