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A047251 Numbers that are congruent to {1, 3, 4, 5} (mod 6). 4
1, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 23, 25, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 43, 45, 46, 47, 49, 51, 52, 53, 55, 57, 58, 59, 61, 63, 64, 65, 67, 69, 70, 71, 73, 75, 76, 77, 79, 81, 82, 83, 85, 87, 88, 89, 91, 93, 94, 95, 97, 99 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
"Polyrhythmic Sequence" P(2,3): numbers congruent to 1 (mod 2) and 1 (mod 3). (See A267027 for definition and description.) - Bob Selcoe, Jan 12 2016
LINKS
FORMULA
From R. J. Mathar, Oct 08 2011: (Start)
a(n) = 3*n/2 - 1/2 - cos(Pi*n/2)/2.
G.f.: x*(x^3+x+1)/((x-1)^2*(x^2+1)). (End)
a(n) = (-2 - (-i)^n - i^n + 6n)/4, with i=sqrt(-1). - Colin Barker, Oct 19 2015
From Wesley Ivan Hurt, May 31 2016: (Start)
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.
a(2k) = A047270(k), a(2k-1) = A016777(k-1) for n>0. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 5*sqrt(3)*Pi/36 - log(2)/3 + log(3)/4. - Amiram Eldar, Dec 17 2021
MAPLE
A047251:=n->(-2-(-I)^n-I^n+6*n)/4: seq(A047251(n), n=1..100); # Wesley Ivan Hurt, May 31 2016
MATHEMATICA
Select[Range[0, 200], MemberQ[{1, 3, 4, 5}, Mod[#, 6]] &] (* Vincenzo Librandi, Jan 12 2016 *)
LinearRecurrence[{2, -2, 2, -1}, {1, 3, 4, 5}, 70] (* Harvey P. Dale, Feb 27 2024 *)
PROG
(PARI) a(n) = (-2-(-I)^n-I^n+6*n)/4 \\ Colin Barker, Oct 19 2015
(PARI) Vec(x*(x^3+x+1)/((x-1)^2*(x^2+1)) + O(x^100)) \\ Colin Barker, Oct 19 2015
(Magma) [n: n in [0..150]|n mod 6 in {1, 3, 4, 5}]; // Vincenzo Librandi, Jan 12 2016
CROSSREFS
Sequence in context: A273670 A153329 A213637 * A258932 A183213 A183172
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified April 22 09:42 EDT 2024. Contains 371894 sequences. (Running on oeis4.)