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A047235 Numbers that are congruent to {2, 4} mod 6. 32
2, 4, 8, 10, 14, 16, 20, 22, 26, 28, 32, 34, 38, 40, 44, 46, 50, 52, 56, 58, 62, 64, 68, 70, 74, 76, 80, 82, 86, 88, 92, 94, 98, 100, 104, 106, 110, 112, 116, 118, 122, 124, 128, 130, 134, 136, 140, 142, 146, 148, 152, 154, 158, 160, 164, 166, 170, 172, 176, 178, 182, 184, 188, 190, 194, 196, 200, 202, 206 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 19 ).

Complement of A047273; A093719(a(n)) = 0. - Reinhard Zumkeller, Oct 01 2008

One could prefix an initial term "1" (or not) and define this sequence through a(n+1) = a(n) + (a(n) mod 6). See A001651 for the analog with 3, A235700 (with 5), A047350 (with 7), A007612 (with 9) and A102039 (with 10). Using 4 or 8 yields a constant sequence from that term on. - M. F. Hasler, Jan 14 2014

Nonnegative m such that m^2/6 + 1/3 is an integer. - Bruno Berselli, Apr 13 2017

Sum_{n>=1} 1/a(n)^2 = Pi^2/27. - Dimitris Valianatos, Oct 10 2017

Numbers divisible by 2 but not by 3. - David James Sycamore, Apr 04 2018

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000

Chunhui Lai, A note on potentially K_4-e graphical sequences, arXiv:math/0308105 [math.CO], 2003.

William A. Stein, The modular forms database

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

FORMULA

a(n) = 2*A001651(n).

n such that phi(3n) = phi(2n). - Benoit Cloitre, Aug 06 2003

G.f.: 2x(1 + x + x^2)/((1 + x)(1 - x)^2). a(n) = 3n - 3/2 - (-1)^n/2. - R. J. Mathar, Nov 22 2008

a(n) = 3n + 5..n odd, 3n + 4..n even a(n) = 6*floor((n+1)/2) + 3 + (-1)^n. - Gary Detlefs, Mar 02 2010

a(n) = 6*n - a(n-1) - 6 (with a(1) = 2). - Vincenzo Librandi, Aug 05 2010

a(n+1) = a(n) + (a(n) mod 6). - M. F. Hasler, Jan 14 2014

MAPLE

seq(6*floor((n+1)/2) +3 + (-1)^n, n= 1..67); # Gary Detlefs, Mar 02 2010

MATHEMATICA

Flatten[Table[{6n - 4, 6n - 2}, {n, 40}]] (* Alonso del Arte, Oct 27 2014 *)

PROG

(MAGMA) [ n eq 1 select 2 else Self(n-1)+2*(1+n mod 2): n in [1..70] ]; // Klaus Brockhaus, Dec 13 2008

(PARI) a(n)=(n-1)\2*6+3+(-1)^n \\ Charles R Greathouse IV, Jul 01 2013

(PARI) first(n) = my(v = vector(n, i, 3*i - 1)); forstep(i = 2, n, 2, v[i]--); v \\ David A. Corneth, Oct 20 2017

CROSSREFS

Equals 2*A001651.

Cf. A007310 [(6*n+(-1)^n-3)/2]. [Bruno Berselli, Jun 24 2010]

Sequence in context: A283967 A232745 A189782 * A328588 A287844 A219696

Adjacent sequences:  A047232 A047233 A047234 * A047236 A047237 A047238

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 11 22:31 EST 2019. Contains 329046 sequences. (Running on oeis4.)