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A227144 Numbers that are congruent to {1, 2, 7, 17, 23} modulo 24. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 31 00:53 EDT 2020. Contains 334747 sequences. (Running on oeis4.)