A227144 Numbers that are congruent to {1, 2, 7, 17, 23} modulo 24.
1, 2, 7, 17, 23, 25, 26, 31, 41, 47, 49, 50, 55, 65, 71, 73, 74, 79, 89, 95, 97, 98, 103, 113, 119, 121, 122, 127, 137, 143, 145, 146, 151, 161, 167, 169, 170, 175, 185, 191, 193, 194, 199, 209, 215, 217, 218, 223, 233, 239, 241, 242, 247, 257, 263, 265, 266
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).
Programs
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Haskell
a227144 n = a227144_list !! (n-1) a227144_list = [1,2,7,17,23] ++ map (+ 24) a227144_list
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Magma
[n : n in [0..300] | n mod 24 in [1, 2, 7, 17, 23]]; // Wesley Ivan Hurt, Dec 26 2016
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Maple
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
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Mathematica
Select[Range[500], MemberQ[{1, 2, 7, 17, 23}, Mod[#, 24]] &] (* Wesley Ivan Hurt, Dec 26 2016 *) LinearRecurrence[{1,0,0,0,1,-1},{1,2,7,17,23,25},60] (* Harvey P. Dale, Dec 18 2019 *) -
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
Formula
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
From Wesley Ivan Hurt, Dec 26 2016: (Start)
a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.
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.
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)
Comments