A345332 a(n) is the number of consecutive even prime gap pairs (g1, g2) satisfying g1 == 0 (mod 6) and g2 == 0 (mod 6) out of the first 2^n consecutive even prime gap pairs.

0, 0, 0, 0, 1, 1, 6, 14, 28, 53, 122, 275, 597, 1203, 2456, 5111, 10573, 21662, 44553, 91246, 185422, 377264, 765956, 1552001, 3140326, 6349270, 12825847, 25891832

Offset

0,7

Comments

It seems that the fraction of prime gap pairs (g1, g2) for which g1 == 0 (mod 6), satisfying g2 == 0 (mod 6) as well, i.e., a(n)/A340948(n), tends to a constant, say c, when the number of prime gap pairs tends to infinity. From n = 27 we obtain that c > 0.431, while it can be argued heuristically that c < 0.5.

Meanwhile, the fractions of prime gap pairs (g1, g2), satisfying either g2 == 2 (mod 6) or g2 == 4 (mod 6), seem to tend both to another constant, (1-c)/2, when the number of prime gap pairs tends to infinity (see A345333 and A345334).

Links

Table of n, a(n) for n=0..27.

Formula

a(n) = A340948(n) - (A345333(n) + A345334(n)).

Crossrefs

Cf. A340948, A341531, A341532, A345333, A345334.

Sequence in context: A128806 A139596 A192035 * A183023 A284246 A210000

Adjacent sequences: A345329 A345330 A345331 * A345333 A345334 A345335

Keyword

nonn,more

Author

A.H.M. Smeets, Jun 14 2021

Status

approved