A388068 Twin primes in the twin prime partitions defined in A381169 that contain one twin prime pair.

3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 311, 313, 347, 349, 461, 463, 1091, 1093, 1151, 1153, 1787, 1789, 2381, 2383, 3557, 3559, 3581, 3583, 3671, 3673, 4049, 4051, 4337, 4339, 5099, 5101, 5741, 5743, 6197, 6199, 6359, 6361, 6449, 6451, 6827, 6829, 6869, 6871

Offset

1,1

Comments

These are the "lonely twin primes" in terms of the distance between twin prime pairs, while the lonely twin primes defined in A069453 are those without adjacent twin primes.

Links

Table of n, a(n) for n=1..49.

Prog

(Python)
from sympy import isprime, nextprime
def nexttwin(x):
    p1 = nextprime(x); t1 = p1 + 2
    while isprime(t1) == 0: p1 = nextprime(t1); t1 = p1 + 2
    return p1+1
print(3, end = ', '); L = [4]
while L[0] < 6870:
    t0 = L[-1]; t1 = nexttwin(t0); g0 = t1 - t0; M = [t1]; t = nexttwin(t1); g1 = t - t1
    while g1 < g0 and t - t1 <= g1: M.append(t); t1 = t; t = nexttwin(t)
    if len(M) == 1: print(M[0]-1, M[0]+1, sep = ', ', end = ', ')
    L = M

Crossrefs

Cf. A069453, A381169.

Sequence in context: A132143 A239879 A001097 * A117243 A179679 A059362

Adjacent sequences: A388065 A388066 A388067 * A388069 A388070 A388071

Keyword

nonn

Author

Ya-Ping Lu, Oct 14 2025

Status

approved