A203016 Numbers congruent to {1, 2, 3, 4} mod 6, multiplied by 3.

3, 6, 9, 12, 21, 24, 27, 30, 39, 42, 45, 48, 57, 60, 63, 66, 75, 78, 81, 84, 93, 96, 99, 102, 111, 114, 117, 120, 129, 132, 135, 138, 147, 150, 153, 156, 165, 168, 171, 174, 183, 186, 189, 192, 201, 204, 207, 210, 219, 222, 225, 228, 237, 240, 243, 246, 255, 258, 261, 264, 273, 276, 279, 282, 291, 294, 297

Offset

1,1

Comments

Appears to coincide with the list of numbers n such that A006600(n) is not a multiple of n. Equals A047227 multiplied by 3.

Links

Table of n, a(n) for n=1..67.

Colin Foster, Peripheral mathematical knowledge, For the Learning of Mathematics, vol. 31, #3 (November, 2011), pp. 24-28.

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

Formula

From Wesley Ivan Hurt, Jun 07 2016: (Start)

G.f.: 3*x*(1+x+x^2+x^3+2*x^4)/((x-1)^2*(1+x+x^2+x^3)).

a(n) = 3*(6*n-5-i^(2*n)+(1+i)*i^(1-n)+(1-i)*i^(n-1))/4 where i=sqrt(-1).

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(2k) = 3*A047235(k), a(2k-1) = 3*A047241(k). (End)

E.g.f.: 3*(4 + sin(x) - cos(x) + (3*x - 2)*sinh(x) + 3*(x - 1)*cosh(x))/2. - Ilya Gutkovskiy, Jun 07 2016

Maple

A203016:=n->3*(6*n-5-I^(2*n)+(1+I)*I^(1-n)+(1-I)*I^(n-1))/4: seq(A203016(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

Mathematica

3 Select[Range[100], MemberQ[{1, 2, 3, 4}, Mod[#, 6]] &] (* Wesley Ivan Hurt, Jun 07 2016 *)

Prog

(Magma) [3*n : n in [0..100] | n mod 6 in [1..4]]; // Wesley Ivan Hurt, Jun 07 2016

Crossrefs

Cf. A006600, A047227, A047235, A047241.

Sequence in context: A175589 A348339 A282759 * A153838 A143829 A194420

Adjacent sequences: A203013 A203014 A203015 * A203017 A203018 A203019

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 27 2011

Status

approved