A344117 Number of twin prime pairs in the range (6*n + 1, 6*(n + m) + 1], where m is the number of twin prime pairs, 6*k +- 1 for k = 1, 2, ..., n.

1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 3, 3, 4, 4, 3, 3, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 4, 4, 4, 3, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5

Offset: 1

Author

Ya-Ping Lu, Jun 24 2021

Keywords

• nonn

Comments

Conjecture: a(n) >= 1.

Crossrefs

Cf. A071538, A079629, A080356, A237840, A332086, A337788.

Programs

Python

from sympy import isprime
def istwin(m): return 1 if isprime(6*m-1)*isprime(6*m+1) == 1 else 0
ct1 = 0
for n in range(1, 100):
    ct1 += istwin(n); ct = 0
    for m in range (n + 1, n + ct1 + 1): ct += istwin(m)
    print(ct)