[go: up one dir, main page]

login
A317657
Numbers congruent to {15, 75, 95} mod 100.
0
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, ... ).
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
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Aug 03 2018
STATUS
approved