cp's OEIS Frontend

A317657 Numbers congruent to {15, 75, 95} mod 100.

%I A317657 #25 Jan 27 2020 11:14:43
%S A317657 15,75,95,115,175,195,215,275,295,315,375,395,415,475,495,515,575,595,
%T A317657 615,675,695,715,775,795,815,875,895,915,975,995,1015,1075,1095,1115,
%U A317657 1175,1195,1215,1275,1295,1315,1375,1395,1415,1475,1495,1515
%N A317657 Numbers congruent to {15, 75, 95} mod 100.
%C A317657 Numbers written in French ending in "quinze".
%C A317657 a(n) = 5 * (3, 15, 19, 23, 35, 39, 43, 55, 59, ... ).
%H A317657 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1)
%F A317657 a(n) = 10*A317633(n) + 5.
%F A317657 a(n) = a(n-3) + 100, a(1) = 15, a(2) = 75, a(3) = 95.
%F A317657 From _Franck Maminirina Ramaharo_, Aug 05 2018: (Start)
%F A317657 a(n) = a(n-1) + a(n-3) - a(n-4), n>4.
%F A317657 a(n) = A290781(A047205(n)).
%F A317657 a(n) = 20*A008854(n+1) - 5.
%F A317657 a(n) = 100*n/3 - 80*sin(2*n*Pi/3)/(3*sqrt(3)) - 5.
%F A317657 G.f.: (5*x*(x^3 + 4*x^2 + 12*x + 3))/((x^2 + x + 1)*(x - 1)^2).
%F A317657 E.g.f.: 100*x*exp(x)/3 - 80*sin(sqrt(3)*x/2)/(exp(x/2)*(3*sqrt(3)))-5*exp(x).
%F A317657 (End)
%p A317657 select(n->modp(n,100)=15 or modp(n,100)=75 or modp(n,100)=95,[$0..1520]); # _Muniru A Asiru_, Aug 29 2018
%t A317657 Rest@ CoefficientList[Series[(5 x (x^3 + 4 x^2 + 12 x + 3))/((x^2 + x + 1) (x - 1)^2), {x, 0, 46}], x] (* _Michael De Vlieger_, Aug 05 2018 *)
%t A317657 Table[100*n/3 - 80*Sin[2*n*Pi/3]/(3*Sqrt[3]) - 5,{n,1,46}] (* _Stefano Spezia_, Aug 29 2018 *)
%o A317657 (GAP) Filtered([0..1520], n->n mod 100=15 or n mod 100=75 or n mod 100=95); # _Muniru A Asiru_, Aug 29 2018
%Y A317657 Cf. A008587, A008854, A047205, A090772, A290781, A317633.
%K A317657 nonn,easy
%O A317657 1,1
%A A317657 _Paul Curtz_, Aug 03 2018