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

1,1

Comments

Numbers written in French ending in "quinze".

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

Links

Table of n, a(n) for n=1..46.

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

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)

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A080841 A022675 A214453 * A339518 A296193 A135916

Adjacent sequences: A317654 A317655 A317656 * A317658 A317659 A317660

Keyword

nonn,easy

Author

Paul Curtz, Aug 03 2018

Status

approved