A047487 Numbers that are congruent to {2, 3, 5, 7} mod 8.

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-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

Cf. A004767, A047617.

Sequence in context: A002269 A327445 A325119 * A327203 A048461 A338174

Adjacent sequences: A047484 A047485 A047486 * A047488 A047489 A047490

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved