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A047471
Numbers that are congruent to {1, 3} mod 8.
11
1, 3, 9, 11, 17, 19, 25, 27, 33, 35, 41, 43, 49, 51, 57, 59, 65, 67, 73, 75, 81, 83, 89, 91, 97, 99, 105, 107, 113, 115, 121, 123, 129, 131, 137, 139, 145, 147, 153, 155, 161, 163, 169, 171, 177, 179, 185, 187, 193, 195, 201, 203, 209, 211, 217, 219, 225, 227, 233
OFFSET
1,2
FORMULA
G.f.: x*(1+2*x+5*x^2)/((1+x)*(1-x)^2). - Paul Barry, Apr 10 2008
a(n) = 4*(n-1)-(-1)^n. - Rolf Pleisch, Aug 04 2009
a(n) = 8*n-a(n-1)-12, with a(1)=1. - Vincenzo Librandi, Aug 06 2010
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/8 + sqrt(2)*log(sqrt(2)+1)/4. - Amiram Eldar, Dec 18 2021
EXAMPLE
For n=2, a(2) = 8*2-1-12 = 3;
For n=3, a(3) = 8*3-3-12 = 9;
For n=4, a(4) = 8*4-9-12 = 11. - Vincenzo Librandi, Aug 06 2010
MAPLE
A047471:=n->4*n - 4 - (-1)^n; seq(A047471(n), n=1..100); # Wesley Ivan Hurt, Jan 30 2014
MATHEMATICA
Table[4 n - 4 - (-1)^n, {n, 100}] (* Wesley Ivan Hurt, Jan 30 2014 *)
#+{1, 3}&/@(8*Range[0, 30])//Flatten (* or *) LinearRecurrence[{1, 1, -1}, {1, 3, 9}, 60] (* Harvey P. Dale, Jan 05 2017 *)
PROG
(Haskell)
a047471 n = a047471_list !! (n-1)
a047471_list = [n | n <- [1..], mod n 8 `elem` [1, 3]]
-- Reinhard Zumkeller, Dec 29 2012
(Magma) [4*(n-1)-(-1)^n : n in [1..80]]; // Wesley Ivan Hurt, Apr 28 2017
CROSSREFS
Union of A017077 and A017101.
Cf. A033200 (primes).
Sequence in context: A310317 A194401 A190238 * A354938 A365082 A201544
KEYWORD
nonn,easy
EXTENSIONS
More terms from Vincenzo Librandi, Aug 06 2010
STATUS
approved