oeis.org

A016969 - OEIS

5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89, 95, 101, 107, 113, 119, 125, 131, 137, 143, 149, 155, 161, 167, 173, 179, 185, 191, 197, 203, 209, 215, 221, 227, 233, 239, 245, 251, 257, 263, 269, 275, 281, 287, 293, 299, 305, 311, 317, 323, 329, 335

COMMENTS

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0(18).

Exponents e such that x^e + x - 1 is reducible.

a(n-1), n >= 1, appears as first column in the triangle A239127 related to the Collatz problem. - Wolfdieter Lang, Mar 14 2014

Numbers that are not divisible by their digital root in base 4. - Amiram Eldar, Nov 24 2022

FORMULA

G.f.: (5+x)/(1-x)^2.

a(0) = 5; for n > 0, a(n) = a(n-1)+6. (End)

a(n) = floor((12n-1)/2) with offset 1..a(1)=5. - Gary Detlefs, Mar 07 2010

a(n) = 4*(3*n+1) - a(n-1) (with a(0) = 5). - Vincenzo Librandi, Nov 20 2010

a(n) = floor(1/(1/sin(1/n) - n)). - Clark Kimberling, Feb 19 2010

a(n) = 3*Sum_{k = 0..n} binomial(6*n+5, 6*k+2)*Bernoulli(6*k+2). - Michel Marcus, Jan 11 2016

a(n) = 2*A000217(n+2) - 1 - 2*A000217(n-1). See Twin Triangular Frames illustration. - Leo Tavares, Aug 25 2021

Sum_{n>=0} (-1)^n/a(n) = Pi/6 - sqrt(3)*arccoth(sqrt(3))/3. - Amiram Eldar, Dec 10 2021

MATHEMATICA

6Range[0, 59] + 5 (* or *) NestList[6 + # &, 5, 60] (* Harvey P. Dale, Mar 09 2013 *)

CROSSREFS

Cf. A050505 (unlucky numbers).