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A346777 a(n) is the number of consecutive even prime gaps (g1, g2) satisfying g1 == 2 (mod 6) and g2 == 4 (mod 6) out of the first 2^n consecutive even prime gaps. 1
0, 1, 2, 3, 4, 9, 16, 27, 56, 111, 187, 373, 708, 1403, 2780, 5467, 10781, 21248, 41701, 82581, 163473, 323995, 643327, 1278401, 2540048, 5050955, 10052647, 20010073 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
The prime gaps are given in A001223. Here we consider the gaps satisfying the conditions A001223(k) == 2 and A001223(k+1) == 4 (mod 6) for 1 < k <= 2^n + 1.
LINKS
FORMULA
a(n) = A341531(n) - A346776(n) - 1.
EXAMPLE
The sequence A001223(n) mod 6 is given by:
1, 2, 2, 4, 2, 4, 2, 4, 0, 2, 0, 4, 2, 4, 0, 0, 2, 0, 4, 2, 0, 4, 0, 2, ..., denoted here as b(0), b(1), b(2), ..., i.e. b(n) = A001223(n+1) (mod 6) for n >= 0.
The term b(0) is excluded by definition. The conditions b(k) = 2 and b(k+1) == 4 are obtained for k = 2, 4, 6, 12 ...
So a(0) = 0 (k = 2^0 does not occur), a(1) = 1 (one value of k satisfying k <= 2^1), a(2) = 2 (two value of k satisfying k <= 2^2) and a(3) = 3 (three value of k satisfying k <= 2^3).
CROSSREFS
Sequence in context: A354268 A281882 A325436 * A338585 A145027 A088275
KEYWORD
nonn,more
AUTHOR
A.H.M. Smeets, Aug 03 2021
STATUS
approved

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Last modified July 18 21:02 EDT 2024. Contains 374388 sequences. (Running on oeis4.)