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

1,1

Comments

The odd numbers with terminal digit 3 or 9.

Links

Table of n, a(n) for n=1..60.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

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.

a(n) = -A131229(-n+1) with A131229(0) = -3.

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

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 *)

Prog

(Magma) [5*n-(3-(-1)^n)/2: n in [1..60]]; // Vincenzo Librandi, Jan 25 2016

Crossrefs

Cf. A001622, A005408, A045435, A047204, A131229.

Second bisection of A045572.

Sequence in context: A095234 A240240 A032415 * A190745 A075318 A171101

Adjacent sequences: A268041 A268042 A268043 * A268045 A268046 A268047

Keyword

nonn,easy

Author

Mikk Heidemaa, Jan 25 2016

Extensions

Edited by Bruno Berselli, Jan 25 2016

Status

approved