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A203016 Numbers congruent to {1, 2, 3, 4} mod 6, multiplied by 3. 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 (list; graph; refs; listen; history; text; internal format)
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: A109657 A175589 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

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Last modified February 20 01:17 EST 2018. Contains 299357 sequences. (Running on oeis4.)