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A268044 The odd numbers congruent to {3, 4} mod 5. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The odd numbers with terminal digit 3 or 9.
LINKS
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
Second bisection of A045572.
Sequence in context: A095234 A240240 A032415 * A190745 A075318 A171101
KEYWORD
nonn,easy
AUTHOR
Mikk Heidemaa, Jan 25 2016
EXTENSIONS
Edited by Bruno Berselli, Jan 25 2016
STATUS
approved

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Last modified February 21 14:36 EST 2024. Contains 370235 sequences. (Running on oeis4.)