A346399 a(n) is the number of symmetrically distributed consecutive primes centered at n (including n itself if n is prime).

0, 1, 1, 2, 3, 2, 1, 0, 4, 0, 1, 6, 1, 0, 6, 0, 1, 4, 1, 0, 2, 0, 1, 0, 0, 2, 0, 0, 1, 10, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 1, 6, 1, 0, 2, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1, 4, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 1, 0, 4, 0, 1, 0, 0, 2, 0

Offset: 1

Author

Ya-Ping Lu, Sep 18 2021

Keywords

• nonn

Comments

a(n) is the number of consecutive primes in Goldbach pairs of 2n centered at n.

a(n) is odd if n is prime; otherwise, a(n) is even.

n is prime if a(n) = 1 and n is composite if a(n) = 0.

a(n) = 14 is not seen until n = 8021811 (with none higher through 4*10^7). - Bill McEachen, Jul 26 2024

Examples

			a(1) = 0 because no prime is <= 1.
a(2) = 1 because no prime is < 2 and {2} is the only symmetrically distributed prime centered at 2.
a(30) = 10 because there are 10 symmetrically distributed consecutive primes, {13, 17, 19, 23, 29, 31, 37, 41, 43, 47}, centered at 30.
		

Links

• Jason Yuen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A045917, A050237, A060863, A122821.

Programs

Python

from sympy import isprime
for n in range(1, 100):
    d = 1 if n%2 == 0 else 2
    ct = 1 if isprime(n) else 0
    while n - d > 2:
        k = isprime(n+d) + isprime(n-d)
        if k == 2: ct += 2
        elif k == 1: break
        d += 2
    print(ct)