|
|
A273669
|
|
Decimal representation ends with either 2 or 9.
|
|
15
|
|
|
2, 9, 12, 19, 22, 29, 32, 39, 42, 49, 52, 59, 62, 69, 72, 79, 82, 89, 92, 99, 102, 109, 112, 119, 122, 129, 132, 139, 142, 149, 152, 159, 162, 169, 172, 179, 182, 189, 192, 199, 202, 209, 212, 219, 222, 229, 232, 239, 242, 249, 252, 259, 262, 269, 272, 279, 282, 289, 292, 299, 302, 309, 312, 319, 322, 329, 332, 339
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 10*(((n-2)+A000035(n))/2) + 2 [when n is odd], or + 9 [when n is even].
For n >= 5, a(n) = 2*a(n-2) - a(n-4).
Other identities. For all n >= 1:
G.f.: x*(x^2+7*x+2)/((x+1)*(x-1)^2).
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt((1+1/sqrt(5))/2)*phi^2*Pi/10 - log(phi)/(2*sqrt(5)) - log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023
|
|
MATHEMATICA
|
Select[Range@ 340, MemberQ[{2, 9}, Mod[#, 10]] &] (* or *)
Table[{10 n + 2, 10 n + 9}, {n, 0, 33}] // Flatten (* or *)
CoefficientList[Series[(-5/(1 - x) + (11 - x)/(-1 + x)^2 - 2/(1 + x))/2, {x, 0, 67}], x] (* Michael De Vlieger, Aug 07 2016 *)
|
|
PROG
|
(Scheme)
(define (A273669 n) (+ (* 10 (/ (+ (- n 2) (if (odd? n) 1 0)) 2)) (if (odd? n) 2 9)))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|