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A016969
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a(n) = 6*n + 5.
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51
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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
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OFFSET
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0,1
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COMMENTS
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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 (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
Numbers congruent to {5,11} mod 12. - Gary Detlefs, Mar 07 2010
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
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LINKS
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Table of n, a(n) for n=0..55.
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., 36 (1935), 637-649.
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N))
William A. Stein, The modular forms database
Index entries for linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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f[n_]:=6*n+5; lst={}; Do[a=f[n]; AppendTo[lst, a], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 25 2009 *)
6*Range[0, 60]+5 (* or *) NestList[6+#&, 5, 60] (* Harvey P. Dale, Mar 09 2013 *)
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PROG
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(MAGMA) [ 6*n+5: n in [0..55] ]; // Klaus Brockhaus, Jan 04 2009
(Sage) [i+5 for i in range(338) if gcd(i, 6) == 6] # Zerinvary Lajos, May 20 2009
(PARI) a(n)=6*n+5 \\ Charles R Greathouse IV, Jul 10 2016
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CROSSREFS
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Cf. A111863, A007310, A008588, A016921, A016933, A016945, A016957.
Cf. A050505 Unlucky numbers.
Sequence in context: A059538 A172337 A101328 * A007528 A144918 A144920
Adjacent sequences: A016966 A016967 A016968 * A016970 A016971 A016972
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Klaus Brockhaus, Jan 04 2009
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STATUS
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approved
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