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A345334
a(n) is the number of consecutive even prime gap pairs (g1, g2) satisfying g1 == 0 (mod 6) and g2 == 4 (mod 6) out of the first 2^n consecutive even prime gap pairs.
5
0, 0, 0, 0, 1, 3, 6, 14, 28, 58, 132, 254, 515, 1042, 2088, 4172, 8337, 16720, 33556, 66947, 134088, 268036, 535435, 1069932, 2139357, 4275948, 8544351, 17076036
OFFSET
1,6
COMMENTS
It seems that the fraction of prime gap pairs (g1, g2) for which g1 == 0 (mod 6), satisfying g2 == 4 (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) - A345333(n) will change sign infinitely often.
FORMULA
a(n) = A340948(n) - (A345332(n) + A345333(n)).
CROSSREFS
KEYWORD
nonn,more
AUTHOR
A.H.M. Smeets, Jun 14 2021
STATUS
approved