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A047487
Numbers that are congruent to {2, 3, 5, 7} mod 8.
1
2, 3, 5, 7, 10, 11, 13, 15, 18, 19, 21, 23, 26, 27, 29, 31, 34, 35, 37, 39, 42, 43, 45, 47, 50, 51, 53, 55, 58, 59, 61, 63, 66, 67, 69, 71, 74, 75, 77, 79, 82, 83, 85, 87, 90, 91, 93, 95, 98, 99, 101, 103, 106, 107, 109, 111, 114, 115, 117, 119, 122, 123
OFFSET
1,1
FORMULA
From Colin Barker, May 14 2012: (Start)
a(n) = (-3-(-1)^n+i*(-i)^n-i*i^n+8*n)/4 where i=sqrt(-1).
G.f.: x*(2+x+2*x^2+2*x^3+x^4)/((1-x)^2*(1+x)*(1+x^2)). (End)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Vincenzo Librandi, May 17 2012
a(2k) = A004767(k-1) for n>0, a(2k-1) = A047617(k). - Wesley Ivan Hurt, Jun 01 2016
E.g.f.: (2 + sin(x) + (4*x - 1)*sinh(x) + (4*x - 2)*cosh(x))/2. - Ilya Gutkovskiy, Jun 02 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (4-sqrt(2))*Pi/16 - log(2)/8 + sqrt(2)*log(sqrt(2)-1)/8. - Amiram Eldar, Dec 25 2021
MAPLE
A047487:=n->(-3-(-1)^n+I*(-I)^n-I*I^n+8*n)/4: seq(A047487(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016
MATHEMATICA
Select[Range[0, 300], MemberQ[{2, 3, 5, 7}, Mod[#, 8]]&] (* Vincenzo Librandi, May 17 2012 *)
PROG
(Magma) I:=[2, 3, 5, 7, 10]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, May 17 2012
(PARI) my(x='x+O('x^100)); Vec(x*(2+x+2*x^2+2*x^3+x^4)/((1-x)^2*(1+x)*(1+x^2))) \\ Altug Alkan, Dec 24 2015
CROSSREFS
Sequence in context: A327445 A325119 A373487 * A327203 A048461 A338174
KEYWORD
nonn,easy
STATUS
approved