A045803 - OEIS

%I #26 Dec 24 2015 12:02:01

%S 17,19,31,33,117,119,131,133,217,219,231,233,317,319,331,333,417,419,

%T 431,433,517,519,531,533,617,619,631,633,717,719,731,733,817,819,831,

%U 833,917,919,931,933,1017,1019,1031,1033,1117,1119,1131,1133,1217,1219

%N 3-ish numbers (end in 17, 19, 31, 33).

%H Reinhard Zumkeller, <a href="/A045803/b045803.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F G.f.: x*(17+2*x+12*x^2+2*x^3+67*x^4)/(1-x-x^4+x^5). - _Colin Barker_, Jan 23 2012

%F a(n) = -75/2 - (23*(-1)^n)/2 - (9-9*i)*(-i)^n - (9+9*i)*i^n + 25*n where i=sqrt(-1). - _Colin Barker_, Oct 16 2015

%t Select[Range[1300],MemberQ[{17,19,31,33},Mod[#,100]]&] (* or *) LinearRecurrence[{1,0,0,1,-1},{17,19,31,33,117},50] (* _Harvey P. Dale_, Dec 17 2014 *)

%o (Haskell)

%o import Data.List (findIndices)

%o a045803 n = a045803_list !! (n-1)

%o a045803_list = findIndices (`elem` [17,19,31,33]) $ cycle [0..99]

%o -- _Reinhard Zumkeller_, Jan 23 2012

%o (PARI) a(n) = -75/2 - (23*(-1)^n)/2 - (9-9*I)*(-I)^n - (9+9*I)*I^n + 25*n \\ _Colin Barker_, Oct 16 2015

%o (PARI) Vec(x*(17+2*x+12*x^2+2*x^3+67*x^4)/(1-x-x^4+x^5) + O(x^100)) \\ _Colin Barker_, Oct 16 2015

%Y Cf. A045800-A045809.

%Y Cf. A045572, A045797, A045798.

%K nonn,base,easy

%O 1,1

%A _J. H. Conway_

%E More terms from _Erich Friedman_