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

15, 75, 95, 115, 175, 195, 215, 275, 295, 315, 375, 395, 415, 475, 495, 515, 575, 595, 615, 675, 695, 715, 775, 795, 815, 875, 895, 915, 975, 995, 1015, 1075, 1095, 1115, 1175, 1195, 1215, 1275, 1295, 1315, 1375, 1395, 1415, 1475, 1495, 1515

Offset: 1

Author

Paul Curtz, Aug 03 2018

Keywords

• nonn
• easy

Comments

Numbers written in French ending in "quinze".

a(n) = 5 * (3, 15, 19, 23, 35, 39, 43, 55, 59, ... ).

Links

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

Crossrefs

Cf. A008587, A008854, A047205, A090772, A290781, A317633.

Programs

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

Maple

select(n->modp(n,100)=15 or modp(n,100)=75 or modp(n,100)=95,[$0..1520]); # Muniru A Asiru, Aug 29 2018

Mathematica

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 *)
Table[100*n/3 - 80*Sin[2*n*Pi/3]/(3*Sqrt[3]) - 5,{n,1,46}] (* Stefano Spezia, Aug 29 2018 *)

Formula

a(n) = 10*A317633(n) + 5.

a(n) = a(n-3) + 100, a(1) = 15, a(2) = 75, a(3) = 95.

From Franck Maminirina Ramaharo, Aug 05 2018: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4), n>4.

a(n) = A290781(A047205(n)).

a(n) = 20*A008854(n+1) - 5.

a(n) = 100*n/3 - 80*sin(2*n*Pi/3)/(3*sqrt(3)) - 5.

G.f.: (5*x*(x^3 + 4*x^2 + 12*x + 3))/((x^2 + x + 1)*(x - 1)^2).

E.g.f.: 100*x*exp(x)/3 - 80*sin(sqrt(3)*x/2)/(exp(x/2)*(3*sqrt(3)))-5*exp(x).

(End)