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A047263 Numbers that are congruent to {0, 1, 2, 4, 5} mod 6. 4
0, 1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Complement of A016945. - R. J. Mathar, Feb 25 2008

Nonnegative integers m such that floor(2*m^2/12) = 2*floor(m^2/12). See the Crossrefs field of A265187 for similar sequences. - Bruno Berselli, Dec 08 2015

Also, numbers k such that Fibonacci(k) mod 4 = 0, 1 or 3. - Bruno Berselli, Oct 17 2017

LINKS

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

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

FORMULA

O.g.f.: x*(x^2+1)*(x^2+x+1)/((x-1)^2*(x^4+x^3+x^2+x+1)). - R. J. Mathar, Feb 25 2008

a(n) = a(n-5) + 6 for n > 5. - R. J. Mathar, Feb 25 2008

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6. - Harvey P. Dale, Oct 05 2014

From Wesley Ivan Hurt, Aug 16 2016: (Start)

a(n) = n + floor((n-4)/5).

a(n) = (6*n - 4 - ((n+1) mod 5))/5.

a(5k) = 6k-1, a(5k-1) = 6k-2, a(5k-2) = 6k-4, a(5k-3) = 6k-5, a(5k-4) = 6k-6. (End)

MAPLE

for n from 0 to 200 do if n mod 6 <> 3 then printf(`%d, `, n) fi: od:

A047263:=n->6*floor(n/5)+[0, 1, 2, 4, 5][(n mod 5)+1]: seq(A047263(n), n=0..100); # Wesley Ivan Hurt, Aug 16 2016

MATHEMATICA

Select[Range[0, 100], Mod[#, 6]!=3&] (* Harvey P. Dale, May 17 2011 *)

LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 5, 6}, 90] (* Harvey P. Dale, Oct 05 2014 *)

PROG

(MAGMA) [n : n in [0..100] | n mod 6 in [0, 1, 2, 4, 5]]; // Wesley Ivan Hurt, Aug 16 2016

(PARI) first(n) = {select(x->(x%6!=3), vector(6*n\5, i, i-1))} \\ David A. Corneth, Oct 17 2017

CROSSREFS

Cf. A016945, A265187.

Sequence in context: A139143 A183571 A184528 * A039244 A160044 A180917

Adjacent sequences:  A047260 A047261 A047262 * A047264 A047265 A047266

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 11 1999

EXTENSIONS

More terms from James A. Sellers, Feb 19 2001

STATUS

approved

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Last modified October 17 01:37 EDT 2018. Contains 316275 sequences. (Running on oeis4.)