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A047261 Numbers that are congruent to {2, 4, 5} mod 6. 8
2, 4, 5, 8, 10, 11, 14, 16, 17, 20, 22, 23, 26, 28, 29, 32, 34, 35, 38, 40, 41, 44, 46, 47, 50, 52, 53, 56, 58, 59, 62, 64, 65, 68, 70, 71, 74, 76, 77, 80, 82, 83, 86, 88, 89, 92, 94, 95, 98, 100, 101, 104, 106, 107, 110, 112, 113, 116, 118, 119, 122, 124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A214090(a(n)) = 1. - Reinhard Zumkeller, Jul 06 2012

If B and C are terms in the sequence then 2*B*C is a term. B (resp. C) is a term iff B (resp. C) mod 6 = 2, 4 or 5. It follows that (2*B*C) mod 6 = (2*(B mod 6)*(C mod 6)) mod 6 = 2 or 4 and therefore 2*B*C is a term. Examples: for B=16 and C=29, 2*16*29 = 928 is a term: (2*B*C) mod 6 = (2*16*29) mod 6 = 4; (2*2*2) mod 6 = 2. - Jerzy R Borysowicz, May 24 2018

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

FORMULA

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

From Wesley Ivan Hurt, Jun 14 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = (6*n - 1 - 2*cos(2*n*Pi/3))/3.

a(3k) = 6k-1, a(3k-1) = 6k-2, a(3k-2) = 6k-4. (End)

MAPLE

A047261:=n->(6*n-1-2*cos(2*n*Pi/3))/3: seq(A047261(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016

MATHEMATICA

CoefficientList[Series[(1 + x)*(x^2 + 2)/((1 + x + x^2)*(x - 1)^2), {x, 0, 50}], x] (* Wesley Ivan Hurt, Aug 16 2014 *)

Select[ Range@ 125, MemberQ[{2, 4, 5}, Mod[#, 6]] &] (* or *)

LinearRecurrence[{1, 0, 1, -1}, {2, 4, 5, 8}, 62] (* Robert G. Wilson v, Jun 13 2018 *)

PROG

(Haskell)

a047261 n = a047261_list !! n

a047261_list = 2 : 4 : 5 : map (+ 6) a047261_list

-- Reinhard Zumkeller, Feb 19 2013, Jul 06 2012

(MAGMA) [n : n in [0..150] | n mod 6 in [2, 4, 5]]; // Wesley Ivan Hurt, Jun 14 2016

CROSSREFS

Cf. A047242 (complement).

Cf. A007310, A047228, A047241, A047273, A056970, A214090.

Sequence in context: A191987 A138007 A284880 * A286687 A190807 A289058

Adjacent sequences:  A047258 A047259 A047260 * A047262 A047263 A047264

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wesley Ivan Hurt, Aug 16 2014

STATUS

approved

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Last modified August 20 05:25 EDT 2019. Contains 326139 sequences. (Running on oeis4.)