A113802 Numbers that are congruent to {2, 12} mod 14.

2, 12, 16, 26, 30, 40, 44, 54, 58, 68, 72, 82, 86, 96, 100, 110, 114, 124, 128, 138, 142, 152, 156, 166, 170, 180, 184, 194, 198, 208, 212, 222, 226, 236, 240, 250, 254, 264, 268, 278, 282, 292, 296, 306, 310, 320, 324, 334, 338, 348, 352, 362, 366, 376, 380

Offset

1,1

Links

Table of n, a(n) for n=1..55.

Formula

a(n) = 14*n - a(n-1) - 14 (with a(1) = 2). - Vincenzo Librandi, Nov 13 2010

From Wolfdieter Lang, Dec 15 2011: (Start)

a(n) = 7*n-(7-3*(-1)^n)/2.

O.g.f.: 2*x*(1+5*x+x^2)/((1+x)*(1-x)^2).

See the contribution of Bruno Berselli under A113801. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = cot(Pi/7)*Pi/14. - Amiram Eldar, Dec 30 2021

From Amiram Eldar, Nov 25 2024: (Start)

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

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

Mathematica

Select[Range[400], MemberQ[{2, 12}, Mod[#, 14]]&] (* Harvey P. Dale, Oct 30 2011 *)

Crossrefs

Second row A113807.

Cf. A008589, A113801, A113803, A113804, A113805, A113806.

Sequence in context: A298001 A071566 A295821 * A274890 A327570 A057123

Adjacent sequences: A113799 A113800 A113801 * A113803 A113804 A113805

Keyword

nonn,easy

Author

Giovanni Teofilatto, Jan 22 2006

Status

approved