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A113805
Numbers that are congruent to {5, 9} mod 14.
6
5, 9, 19, 23, 33, 37, 47, 51, 61, 65, 75, 79, 89, 93, 103, 107, 117, 121, 131, 135, 145, 149, 159, 163, 173, 177, 187, 191, 201, 205, 215, 219, 229, 233, 243, 247, 257, 261, 271, 275, 285, 289, 299, 303, 313, 317, 327, 331, 341, 345, 355, 359, 369
OFFSET
1,1
FORMULA
a(n) = 14*n - a(n-1) - 14 (with a(1) = 5). - Vincenzo Librandi, Nov 13 2010
From Wolfdieter Lang, Dec 15 2011: (Start)
a(n) = 7*n-(7+3*(-1)^n)/2.
O.g.f.: x*(5+4*x+5*x^2)/((1+x)*(1-x)^2).
See the Bruno Berselli contribution under A113801. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = tan(Pi/7)*Pi/14. - Amiram Eldar, Dec 30 2021
From Amiram Eldar, Nov 25 2024: (Start)
Product_{n>=1} (1 - (-1)^n/a(n)) = 4*sin(Pi/7)*sin(3*Pi/14).
Product_{n>=1} (1 + (-1)^n/a(n)) = 2*sin(Pi/7). (End)
MATHEMATICA
Flatten[Table[14n + {5, 9}, {n, 0, 28}]] (* Alonso del Arte, Dec 15 2011 *)
KEYWORD
nonn,easy
AUTHOR
Giovanni Teofilatto, Jan 22 2006
STATUS
approved