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A016969 a(n) = 6*n + 5. 51

%I

%S 5,11,17,23,29,35,41,47,53,59,65,71,77,83,89,95,101,107,113,119,125,

%T 131,137,143,149,155,161,167,173,179,185,191,197,203,209,215,221,227,

%U 233,239,245,251,257,263,269,275,281,287,293,299,305,311,317,323,329,335

%N a(n) = 6*n + 5.

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

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

%C First differences of A141631 (2, 7, 18). Last digit is period 5: repeat 5, 1, 7, 3, 9, fifth quintuplet with A139788 (1, 7, 3, 9, 5) or A139788(n+4). Three other quintuplets are A139788(n+1) = 7, 3, 9, 5, 1, A139788(n+2) = 3, 9, 5, 1, 7 and A139788(n+3) = 9, 5, 1, 7, 3 (the five odd digits). - _Paul Curtz_, Sep 12 2008

%C Numbers congruent to {5,11} mod 12. - _Gary Detlefs_, Mar 07 2010

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

%C Odd unlucky numbers in A050505. - _Fred Daniel Kline_, Feb 25 2017

%C Intersection of A005408 and A016789. - _Bruno Berselli_, Apr 26 2018

%H Mark W. Coffey, <a href="http://arxiv.org/abs/1601.01673">Bernoulli identities, zeta relations, determinant expressions, Mellin transforms, and representation of the Hurwitz numbers</a>, arXiv:1601.01673 [math.NT], 2016.

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=949">Encyclopedia of Combinatorial Structures 949</a>

%H D. H. Lehmer, <a href="http://www.jstor.org/stable/1968647">Lacunary recurrence formulas for the numbers of Bernoulli and Euler</a>, Annals Math., 36 (1935), 637-649.

%H William A. Stein, <a href="http://modular.math.washington.edu/Tables/dimskg0n.gp">Dimensions of the spaces S_k(Gamma_0(N))</a>

%H William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = A003415(A003415(A125200(n+1)))/2. - _Reinhard Zumkeller_, Nov 24 2006

%F A008615(a(n)) = n+1. - _Reinhard Zumkeller_, Feb 27 2008

%F a(n) = A007310(2*n+1); complement of A016921 with respect to A007310. - _Reinhard Zumkeller_, Oct 02 2008

%F From _Klaus Brockhaus_, Jan 04 2009: (Start)

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

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

%F (End)

%F a(n) = A016921(n)+4 = A016933(n)+3 = A016945(n)+2 = A016957(n)+1. - _Klaus Brockhaus_, Jan 04 2009

%F a(n) = floor((12n-1)/2) with offset 1..a(1)=5. - _Gary Detlefs_, Mar 07 2010

%F a(n) = 4*(3*n+1) - a(n-1) (with a(0)=5). - _Vincenzo Librandi_, Nov 20 2010

%F a(n) = floor(1/(1/sin(1/n) - n)). - _Clark Kimberling_, Feb 19 2010

%F a(n) = 3*Sum_{k=0..n} binomial(6*n+5, 6*k+2)*bernoulli(6*k+2). - _Michel Marcus_, Jan 11 2016

%p a[1]:=-1:for n from 2 to 100 do a[n]:=a[n-1]+6 od: seq(a[n], n=2..47); # _Zerinvary Lajos_, Mar 16 2008

%t f[n_]:=6*n+5; lst={};Do[a=f[n];AppendTo[lst,a],{n,0,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jun 25 2009 *)

%t 6*Range[0,60]+5 (* or *) NestList[6+#&,5,60] (* _Harvey P. Dale_, Mar 09 2013 *)

%o (MAGMA) [ 6*n+5: n in [0..55] ]; // _Klaus Brockhaus_, Jan 04 2009

%o (Sage) [i+5 for i in range(338) if gcd(i,6) == 6] # _Zerinvary Lajos_, May 20 2009

%o (PARI) a(n)=6*n+5 \\ _Charles R Greathouse IV_, Jul 10 2016

%Y Cf. A111863, A007310, A008588, A016921, A016933, A016945, A016957.

%Y Cf. A050505 Unlucky numbers.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Klaus Brockhaus_, Jan 04 2009

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Last modified September 19 08:51 EDT 2018. Contains 315172 sequences. (Running on oeis4.)