A345333 a(n) is the number of consecutive even prime gap pairs (g1, g2) satisfying g1 == 0 (mod 6) and g2 == 2 (mod 6) out of the first 2^n consecutive even prime gap pairs.

0, 0, 0, 1, 2, 4, 7, 16, 32, 62, 131, 264, 537, 1056, 2103, 4207, 8389, 16754, 33521, 67037, 133943, 267788, 535388, 1070008, 2138723, 4275407, 8544670, 17077641

Offset

0,5

Comments

It seems that the fraction of prime gap pairs (g1, g2) for which g1 == 0 (mod 6), satisfying g2 == 2 (mod 6), i.e., a(n)/A340948(n), tends to a constant, say c, when the number of prime gaps tends to infinity. From n = 27 we obtain that c < 0.284, while it can be argued heuristically that c > 0.25.

Futhermore, it is believed that a(n) - A345334(n) will change sign infinitely often.

Links

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

Formula

a(n) = A340948(n) - (A345332(n) + A345334(n)).

Crossrefs

Cf. A340948, A341531, A341532, A345332, A345334.

Sequence in context: A027230 A217929 A320465 * A259544 A294376 A259545

Adjacent sequences: A345330 A345331 A345332 * A345334 A345335 A345336

Keyword

nonn,more

Author

A.H.M. Smeets, Jun 14 2021

Status

approved