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A320427
a(n) = floor(3*n/2) + ceiling(n/6) + 9.
0
11, 13, 14, 16, 17, 19, 21, 23, 24, 26, 27, 29, 31, 33, 34, 36, 37, 39, 41, 43, 44, 46, 47, 49, 51, 53, 54, 56, 57, 59, 61, 63, 64, 66, 67, 69, 71, 73, 74, 76, 77, 79, 81, 83, 84, 86, 87, 89, 91, 93, 94, 96, 97, 99, 101, 103, 104, 106, 107, 109, 111, 113
OFFSET
1,1
COMMENTS
Includes every prime and twin prime (as pairs p, p+2) > 7.
FORMULA
a(n) = -floor((n mod 2)/2 - 5*n/3) + 9.
a(n) = ceiling(5*n/3 - 3/5*(n mod 2)) + 9.
G.f.: (-9*x^6 + 2*x^5 + x^4 + 2*x^3 + x^2 + 2*x + 11)/(x^7 - x^6 - x + 1).
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {11, 13, 14, 16, 17, 19, 21}, 10^3] (* or *)
Table[Floor[3*n/2] + Ceiling[n/6] + 9, {n, 1000}] (* or *)
CoefficientList[Series[(-9*x^6 + 2*x^5 + x^4 + 2*x^3 + x^2 + 2*x + 11)/(x^7 - x^6 - x + 1), {x, 0, 999}], x]
CROSSREFS
Sequence in context: A290468 A129917 A102577 * A038187 A007934 A111347
KEYWORD
nonn,easy
AUTHOR
Mikk Heidemaa, Jan 08 2019
STATUS
approved