A016969 a(n) = 6*n + 5.

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

Offset

0,1

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.

First differences of A141631. - Paul Curtz, Sep 12 2008

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

Odd unlucky numbers in A050505. - Fred Daniel Kline, Feb 25 2017

Intersection of A005408 and A016789. - Bruno Berselli, Apr 26 2018

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

Links

Muniru A Asiru, Table of n, a(n) for n = 0..3000

Mark W. Coffey, Bernoulli identities, zeta relations, determinant expressions, Mellin transforms, and representation of the Hurwitz numbers, arXiv:1601.01673 [math.NT], 2016.

Tanya Khovanova, Recursive Sequences.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 949.

D. H. Lehmer, Lacunary recurrence formulas for the numbers of Bernoulli and Euler, Annals Math., Vol. 36, No. 3 (1935), pp. 637-649.

Amelia Carolina Sparavigna, The Pentagonal Numbers and their Link to an Integer Sequence which contains the Primes of Form 6n-1, Politecnico di Torino (Italy, 2021).

Amelia Carolina Sparavigna, Binary operations inspired by generalized entropies applied to figurate numbers, Politecnico di Torino (Italy, 2021).

William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).

William A. Stein, The modular forms database.

Leo Tavares, Illustration: Twin Triangular Frames.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = A003415(A003415(A125200(n+1)))/2. - Reinhard Zumkeller, Nov 24 2006

A008615(a(n)) = n+1. - Reinhard Zumkeller, Feb 27 2008

a(n) = A007310(2*n+1); complement of A016921 with respect to A007310. - Reinhard Zumkeller, Oct 02 2008

From Klaus Brockhaus, Jan 04 2009: (Start)

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

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

(End)

a(n) = A016921(n)+4 = A016933(n)+3 = A016945(n)+2 = A016957(n)+1. - Klaus Brockhaus, Jan 04 2009

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) = A049452(n+1) / (n+1). - Torlach Rush, Nov 23 2018

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 *)

Prog

(Magma) [ 6*n+5: n in [0..55] ]; // Klaus Brockhaus, Jan 04 2009
(PARI) a(n)=6*n+5 \\ Charles R Greathouse IV, Jul 10 2016
(Scala) (1 to 60).map(6 * _ - 1).mkString(", ") // Alonso del Arte, Nov 23 2018
(GAP) List([0..60], n->6*n+5); # Muniru A Asiru, Nov 24 2018

Crossrefs

Cf. A111863, A007310, A008588, A016921, A016933, A016945, A016957, A049452.

Cf. A050505 (unlucky numbers).

Cf. A000217.

Sequence in context: A059538 A172337 A101328 * A358528 A007528 A144918

Adjacent sequences: A016966 A016967 A016968 * A016970 A016971 A016972

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Klaus Brockhaus, Jan 04 2009

Status

approved