login
A047504
Numbers that are congruent to {1, 2, 3, 4, 5, 7} mod 8.
5
1, 2, 3, 4, 5, 7, 9, 10, 11, 12, 13, 15, 17, 18, 19, 20, 21, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 36, 37, 39, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 63, 65, 66, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 84, 85, 87
OFFSET
1,2
FORMULA
G.f.: x*(1+x^2+x^4+x^5) / ( (x^2-x+1)*(1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Nov 06 2015
From Wesley Ivan Hurt, Jun 16 2016: (Start)
a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-2*a(n-4)+2*a(n-5)-a(n-6) for n>6.
a(n) = (12*n-9+sqrt(3)*(3*sin(n*Pi/3)+sin(2*n*Pi/3)))/9.
a(6k) = 8k-1, a(6k-1) = 8k-3, a(6k-2) = 8k-4, a(6k-3) = 8k-5, a(6k-4) = 8k-6, a(6k-5) = 8k-7. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)+1)*Pi/16 + (3-sqrt(2))*log(2)/8 + sqrt(2)*log(2-sqrt(2))/4. - Amiram Eldar, Dec 28 2021
MAPLE
A047504:=n->(12*n-9+sqrt(3)*(3*sin(n*Pi/3)+sin(2*n*Pi/3)))/9: seq(A047504(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016
MATHEMATICA
Select[Range[0, 100], MemberQ[{1, 2, 3, 4, 5, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)
PROG
(Magma) [n : n in [0..100] | n mod 8 in [1, 2, 3, 4, 5, 7]]; // Wesley Ivan Hurt, Jun 16 2016
CROSSREFS
Cf. A047451 (complement), A047422, A047519.
Sequence in context: A153350 A191919 A039055 * A359830 A088962 A047363
KEYWORD
nonn,easy
STATUS
approved