A360490 a(n) = (1/2) * A241102(n).

109, 433, 172801, 238573, 363313, 640333, 1145773, 1968301, 2056753, 3121201, 3577393, 6588973, 11197873, 13079233, 13381633, 15431473, 21676033, 26462701, 34476301, 37340353, 43823053, 48481201, 54749953, 56454733, 90816013, 96038893, 102667501, 128786113

Offset

1,1

Comments

Primes which are half the difference between 2 cubes of primes.

Primes of the form 3*m^2 + 1, where m is the average of a twin prime pair (A014574).

A subsequence of A243761 and a supersequence of A270249.

Links

Table of n, a(n) for n=1..28.

Formula

a(n) = (1/2) * A241102(n).

Example

172801 is a term because 172801 = (241^3 - 239^3)/2, and 172801, 239 and 241 are all primes.

Prog

(Python)
from itertools import islice
from sympy import isprime, nextprime
def A360490_gen(): # generator of terms
    p, q = 3**3, 5
    while True:
        if isprime(k:=(m:=q**3)-p>>1):
            yield k
        p, q = m, nextprime(q)
A360490_list = list(islice(A360490_gen(), 20)) # Chai Wah Wu, Feb 27 2023

Crossrefs

Cf. A014574, A030078, A103739, A243761, A270249.

Sequence in context: A142846 A166560 A139644 * A270249 A174339 A142640

Adjacent sequences: A360487 A360488 A360489 * A360491 A360492 A360493

Keyword

nonn

Author

Ya-Ping Lu, Feb 09 2023

Status

approved