A268044 The odd numbers congruent to {3, 4} mod 5.
3, 9, 13, 19, 23, 29, 33, 39, 43, 49, 53, 59, 63, 69, 73, 79, 83, 89, 93, 99, 103, 109, 113, 119, 123, 129, 133, 139, 143, 149, 153, 159, 163, 169, 173, 179, 183, 189, 193, 199, 203, 209, 213, 219, 223, 229, 233, 239, 243, 249, 253, 259, 263, 269, 273, 279, 283, 289, 293, 299
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Programs
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Magma
[5*n-(3-(-1)^n)/2: n in [1..60]]; // Vincenzo Librandi, Jan 25 2016
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Mathematica
Table[5 n - (3 - (-1)^n)/2, {n, 1000}] (* or *) Select[ Range [1000], OddQ[#] && MemberQ[{3, 4}, Mod[#, 5]] &] LinearRecurrence[{1,1,-1},{3,9,13},60] (* Harvey P. Dale, Feb 12 2023 *)
Formula
G.f.: x*(3 + 6*x + x^2)/((1 + x)*(1 - x)^2).
a(n) = a(n-1) + a(n-2) - a(n-3).
a(n) = 5*n - (3 - (-1)^n)/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt((5+sqrt(5))/2)*Pi/10 - 3*log(phi)/(2*sqrt(5)), where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023
Extensions
Edited by Bruno Berselli, Jan 25 2016
Comments