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

1,2

Comments

A089911(a(n)) = 1.

Links

Table of n, a(n) for n=1..57.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

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)

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

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 *)

Prog

(Haskell)
a227144 n = a227144_list !! (n-1)
a227144_list = [1, 2, 7, 17, 23] ++ map (+ 24) a227144_list
(Magma) [n : n in [0..300] | n mod 24 in [1, 2, 7, 17, 23]]; // Wesley Ivan Hurt, Dec 26 2016
(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

Crossrefs

Cf. A004771, A089911, A227146.

Sequence in context: A291528 A182575 A074884 * A105911 A038873 A141131

Adjacent sequences: A227141 A227142 A227143 * A227145 A227146 A227147

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jul 05 2013

Status

approved