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

Author

N. J. A. Sloane, Dec 27 2011

Keywords

• nonn
• easy

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

• 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).

Crossrefs

Cf. A006600, A047227, A047235, A047241.

Programs

Magma

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

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