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%I #19 Sep 08 2022 08:46:01
%S 3,6,9,12,21,24,27,30,39,42,45,48,57,60,63,66,75,78,81,84,93,96,99,
%T 102,111,114,117,120,129,132,135,138,147,150,153,156,165,168,171,174,
%U 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
%N Numbers congruent to {1, 2, 3, 4} mod 6, multiplied by 3.
%C Appears to coincide with the list of numbers n such that A006600(n) is not a multiple of n. Equals A047227 multiplied by 3.
%H Colin Foster, <a href="http://www.foster77.co.uk/Foster,%20For%20The%20Learning%20of%20Mathematics,%20Peripheral%20Mathematical%20Knowledge.pdf">Peripheral mathematical knowledge</a>, For the Learning of Mathematics, vol. 31, #3 (November, 2011), pp. 24-28.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F From _Wesley Ivan Hurt_, Jun 07 2016: (Start)
%F G.f.: 3*x*(1+x+x^2+x^3+2*x^4)/((x-1)^2*(1+x+x^2+x^3)).
%F a(n) = 3*(6*n-5-i^(2*n)+(1+i)*i^(1-n)+(1-i)*i^(n-1))/4 where i=sqrt(-1).
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F a(2k) = 3*A047235(k), a(2k-1) = 3*A047241(k). (End)
%F 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
%p 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
%t 3 Select[Range[100], MemberQ[{1, 2, 3, 4}, Mod[#, 6]] &] (* _Wesley Ivan Hurt_, Jun 07 2016 *)
%o (Magma) [3*n : n in [0..100] | n mod 6 in [1..4]]; // _Wesley Ivan Hurt_, Jun 07 2016
%Y Cf. A006600, A047227, A047235, A047241.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Dec 27 2011