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

%I A346399 #57 Jul 27 2024 23:49:04
%S A346399 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,
%T A346399 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,
%U A346399 2,0,1,2,1,0,0,2,0,0,1,0,4,0,1,0,0,2,0
%N A346399 a(n) is the number of symmetrically distributed consecutive primes centered at n (including n itself if n is prime).
%C A346399 a(n) is the number of consecutive primes in Goldbach pairs of 2n centered at n.
%C A346399 a(n) is odd if n is prime; otherwise, a(n) is even.
%C A346399 n is prime if a(n) = 1 and n is composite if a(n) = 0.
%C A346399 a(n) = 14 is not seen until n = 8021811 (with none higher through 4*10^7). - _Bill McEachen_, Jul 26 2024
%H A346399 Jason Yuen, <a href="/A346399/b346399.txt">Table of n, a(n) for n = 1..10000</a>
%e A346399 a(1) = 0 because no prime is <= 1.
%e A346399 a(2) = 1 because no prime is < 2 and {2} is the only symmetrically distributed prime centered at 2.
%e A346399 a(30) = 10 because there are 10 symmetrically distributed consecutive primes, {13, 17, 19, 23, 29, 31, 37, 41, 43, 47}, centered at 30.
%o A346399 (Python)
%o A346399 from sympy import isprime
%o A346399 for n in range(1, 100):
%o A346399     d = 1 if n%2 == 0 else 2
%o A346399     ct = 1 if isprime(n) else 0
%o A346399     while n - d > 2:
%o A346399         k = isprime(n+d) + isprime(n-d)
%o A346399         if k == 2: ct += 2
%o A346399         elif k == 1: break
%o A346399         d += 2
%o A346399     print(ct)
%Y A346399 Cf. A045917, A050237, A060863, A122821.
%K A346399 nonn
%O A346399 1,4
%A A346399 _Ya-Ping Lu_, Sep 18 2021