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A227144 Numbers that are congruent to {1, 2, 7, 17, 23} modulo 24.

%I A227144 #15 Sep 08 2022 08:46:05
%S A227144 1,2,7,17,23,25,26,31,41,47,49,50,55,65,71,73,74,79,89,95,97,98,103,
%T A227144 113,119,121,122,127,137,143,145,146,151,161,167,169,170,175,185,191,
%U A227144 193,194,199,209,215,217,218,223,233,239,241,242,247,257,263,265,266
%N A227144 Numbers that are congruent to {1, 2, 7, 17, 23} modulo 24.
%C A227144 A089911(a(n)) = 1.
%H A227144 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F A227144 G.f.: x*(1+x)*(x^4+5*x^3+5*x^2+1) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - _R. J. Mathar_, Jul 17 2013
%F A227144 From _Wesley Ivan Hurt_, Dec 26 2016: (Start)
%F A227144 a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.
%F A227144 a(n) = (120*n - 110 - 6*(n mod 5) - 26*((n+1) mod 5) - ((n+2) mod 5) + 19*((n+3) mod 5) + 14*((n+4) mod 5))/25.
%F A227144 a(5k) = 24k-1, a(5k-1) = 24k-7, a(5k-2) = 24k-17, a(5k-3) = 24k-22, a(5k-4) = 24k-23. (End)
%p A227144 A227144:=n->24*floor(n/5)+[1, 2, 7, 17, 23][(n mod 5)+1]: seq(A227144(n), n=0..100); # _Wesley Ivan Hurt_, Dec 26 2016
%t A227144 Select[Range[500], MemberQ[{1, 2, 7, 17, 23}, Mod[#, 24]] &] (* _Wesley Ivan Hurt_, Dec 26 2016 *)
%t A227144 LinearRecurrence[{1,0,0,0,1,-1},{1,2,7,17,23,25},60] (* _Harvey P. Dale_, Dec 18 2019 *)
%o A227144 (Haskell)
%o A227144 a227144 n = a227144_list !! (n-1)
%o A227144 a227144_list = [1,2,7,17,23] ++ map (+ 24) a227144_list
%o A227144 (Magma) [n : n in [0..300] | n mod 24 in [1, 2, 7, 17, 23]]; // _Wesley Ivan Hurt_, Dec 26 2016
%o A227144 (PARI) Vec(x*(1+x)*(x^4 +5*x^3 +5*x^2 +1)/((x^4 +x^3 +x^2 +x +1)*(x-1)^2) + O(x^50)) \\ _G. C. Greubel_, Dec 26 2016
%Y A227144 Cf. A004771, A089911, A227146.
%K A227144 nonn,easy
%O A227144 1,2
%A A227144 _Reinhard Zumkeller_, Jul 05 2013