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A047243 Numbers that are congruent to {2, 3} mod 6. 6
2, 3, 8, 9, 14, 15, 20, 21, 26, 27, 32, 33, 38, 39, 44, 45, 50, 51, 56, 57, 62, 63, 68, 69, 74, 75, 80, 81, 86, 87, 92, 93, 98, 99, 104, 105, 110, 111, 116, 117, 122, 123, 128, 129, 134, 135, 140, 141, 146, 147, 152, 153, 158, 159, 164, 165, 170, 171, 176, 177, 182, 183 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Solutions to 3^x - 2^x == 5 (mod 7). - Cino Hilliard, May 09 2003

REFERENCES

Emil Grosswald, Topics From the Theory of Numbers. 1966 p 65 problem 23

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

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

FORMULA

a(n) = 6*n - 7 - a(n-1), with a(1)=2. - Vincenzo Librandi, Aug 05 2010

G.f.: x*(2+x+3*x^2) / ( (1+x)*(1-x)^2 ). - R. J. Mathar, Oct 08 2011

From Guenther Schrack, Jun 21 2019: (Start)

a(n) = a(n-2) + 6 with a(1)=2, a(2)=3 for n > 2;

a(n) = 3*n - 2 - (-1)^n. (End)

E.g.f.: 3 - 3*(1-x)*cosh(x) - (1-3*x)*sinh(x). - G. C. Greubel, Jun 30 2019

MATHEMATICA

Select[Range[0, 210], MemberQ[{2, 3}, Mod[#, 6]] &] (* or *)

Fold[Append[#1, 6 #2 - Last@ #1 - 7] &, {2}, Range[2, 70]] (* or *)

Rest@ CoefficientList[Series[x(2+x+3x^2)/((1+x)(1-x)^2), {x, 0, 70}], x] (* Michael De Vlieger, Jan 12 2018 *)

PROG

(PARI) vector(70, n, 3*n-2-(-1)^n) \\ G. C. Greubel, Jun 30 2019

(MAGMA) [3*n-2-(-1)^n: n in [1..70]]; // G. C. Greubel, Jun 30 2019

(Sage) [3*n-2-(-1)^n for n in (1..70)] # G. C. Greubel, Jun 30 2019

(GAP) List([1..70], n-> 3*n-2-(-1)^n) # G. C. Greubel, Jun 30 2019

CROSSREFS

Cf. A030531. Complement of A047260.

Sequence in context: A281111 A301917 A327312 * A277094 A099148 A309423

Adjacent sequences:  A047240 A047241 A047242 * A047244 A047245 A047246

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Cino Hilliard, May 09 2003

STATUS

approved

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Last modified December 11 18:34 EST 2019. Contains 329925 sequences. (Running on oeis4.)