|
|
A047218
|
|
Numbers that are congruent to {0, 3} mod 5.
|
|
37
|
|
|
0, 3, 5, 8, 10, 13, 15, 18, 20, 23, 25, 28, 30, 33, 35, 38, 40, 43, 45, 48, 50, 53, 55, 58, 60, 63, 65, 68, 70, 73, 75, 78, 80, 83, 85, 88, 90, 93, 95, 98, 100, 103, 105, 108, 110, 113, 115, 118, 120, 123, 125, 128, 130, 133, 135, 138, 140, 143, 145, 148
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Multiples of 5 interleaved with 2 less than multiples of 5. - Wesley Ivan Hurt, Oct 19 2013
Numbers k such that k^2/5 + k*(k + 1)/10 = k*(3*k + 1)/10 is a nonnegative integer. - Bruno Berselli, Feb 14 2017
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2*n - 5 + ceiling(n/2). - Jesus De Loera (deloera(AT)math.ucdavis.edu)
G.f.: (2*x + 3)*x^2/((x + 1)*(x - 1)^2).
a(n) = (10*n + (-1)^n - 9)/4.
a(n) = a(n-1) + a(n-2) - a(n-3). (End)
a(n) = floor(5*n/2)-2 = 3*n - 3 - floor((n-1)/2). - Wesley Ivan Hurt, Oct 14 2013
Sum_{n>=2} (-1)^n/a(n) = log(5)/4 - sqrt(5)*log(phi)/10 - sqrt(1-2/sqrt(5))*Pi/10, where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021
E.g.f.: 2 + ((5*x - 9/2)*exp(x) + (1/2)*exp(-x))/2. - David Lovler, Aug 22 2022
|
|
MAPLE
|
|
|
MATHEMATICA
|
With[{c5=5*Range[0, 30]}, Riffle[c5, c5+3]] (* or *) LinearRecurrence[{1, 1, -1}, {0, 3, 5}, 60] (* Harvey P. Dale, Apr 02 2017 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|