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A047400
Numbers that are congruent to {1, 3, 6} mod 8.
1
1, 3, 6, 9, 11, 14, 17, 19, 22, 25, 27, 30, 33, 35, 38, 41, 43, 46, 49, 51, 54, 57, 59, 62, 65, 67, 70, 73, 75, 78, 81, 83, 86, 89, 91, 94, 97, 99, 102, 105, 107, 110, 113, 115, 118, 121, 123, 126, 129, 131, 134, 137, 139, 142, 145, 147, 150, 153, 155, 158
OFFSET
1,2
COMMENTS
Union of A017077, A017101 and A017137. - R. J. Mathar, Apr 14 2008
FORMULA
a(n) = A004773(n-1) + A004773(n). - Gary W. Adamson, Sep 13 2007
G.f.: x*(1+x)*(2x^2+x+1)/((-1+x)^2*(x^2+x+1)). a(n) = a(n-3)+8 for n>3. - R. J. Mathar, Apr 14 2008
From Wesley Ivan Hurt, Jun 10 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = 2*(12*n-9+sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 8k-2, a(3k-1) = 8k-5, a(3k-2) = 8k-7. (End)
MAPLE
A047400:=n->2*(12*n-9+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047400(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016
MATHEMATICA
Select[Range[0, 150], MemberQ[{1, 3, 6}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)
PROG
(PARI) a(n) = {x=8*floor((n-1)/3); if(n%3==1, x=x+1); if(n%3==2, x=x+3); if(n%3==0, x=x+6); x} \\ Michael B. Porter, Oct 02 2009
(Magma) [n: n in [1..300] | n mod 8 in [1, 3, 6]]; // Vincenzo Librandi, Mar 27 2011
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved