A113806 Numbers that are congruent to {6, 8} mod 14.

6, 8, 20, 22, 34, 36, 48, 50, 62, 64, 76, 78, 90, 92, 104, 106, 118, 120, 132, 134, 146, 148, 160, 162, 174, 176, 188, 190, 202, 204, 216, 218, 230, 232, 244, 246, 258, 260, 272, 274, 286, 288, 300, 302, 314, 316, 328, 330, 342, 344, 356, 358, 370

Offset

1,1

Links

Table of n, a(n) for n=1..53.

Formula

a(n) = 14*n - a(n-1) - 14 (with a(1) = 6). - Vincenzo Librandi, Nov 13 2010

From Wolfdieter Lang, Dec 15 2011: (Start)

a(n) = 7*n-(7+5*(-1)^n)/2.

O.g.f.: 2*x*(3+x+3*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/14)*Pi/14. - Amiram Eldar, Dec 30 2021

From Amiram Eldar, Nov 25 2024: (Start)

Product_{n>=1} (1 - (-1)^n/a(n)) = sec(Pi/14).

Product_{n>=1} (1 + (-1)^n/a(n)) = cosec(Pi/7)*cosec(3*Pi/14)/4. (End)

Mathematica

Flatten[# + {6, 8} &/@ (14 Range[0, 30])] (* Harvey P. Dale, Jan 11 2011 *)

Crossrefs

Cf. A008589, A113801, A113802, A113803, A113804, A113805, A113807.

Sequence in context: A279729 A357946 A309653 * A105775 A159469 A096524

Adjacent sequences: A113803 A113804 A113805 * A113807 A113808 A113809

Keyword

nonn,easy

Author

Giovanni Teofilatto, Jan 22 2006

Status

approved