A066043 a(1) = 1; for m > 0, a(2m) = 2m, a(2m+1) = 4m+2.

1, 2, 6, 4, 10, 6, 14, 8, 18, 10, 22, 12, 26, 14, 30, 16, 34, 18, 38, 20, 42, 22, 46, 24, 50, 26, 54, 28, 58, 30, 62, 32, 66, 34, 70, 36, 74, 38, 78, 40, 82, 42, 86, 44, 90, 46, 94, 48, 98, 50, 102, 52, 106, 54, 110, 56, 114, 58, 118, 60, 122, 62, 126, 64, 130, 66, 134, 68

Offset

1,2

Comments

Length of period of sequences r(k,n) = floor(sinh(1)*k!) - n*floor(sinh(1)*k!/n) when n is fixed. - Benoit Cloitre, Jun 22 2003

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Formula

O.g.f.: (x+2x^2+4x^3-x^5)/(1-x^2)^2. - Len Smiley, Dec 05 2001

a(n)*a(n+3) = -4 + a(n+1)*a(n+2).

From Harry J. Smith, Nov 08 2009: (Start)

a(n) = A109043(n), n > 1.

a(n) = 2*A026741(n), n > 1. (End)

Example

r(k,7) is sequence 1, 2, 0, 0, 1, 6, 1, 1, 3, 2, 2, 3, 5, 0, 1, 2, 0, 0, 1, 6, 1, 1, 3, 2, 2, 3, 5, 0.... which is periodic with period (1, 2, 0, 0, 1, 6, 1, 1, 3, 2, 2, 3, 5, 0) of length 14 = a(7).

Mathematica

Join[{1}, LCM[Range[2, 100], 2]] (* Paolo Xausa, Feb 19 2024 *)

Prog

(PARI) a(n)=if(n<2, 1, if(n%2, 2*n, n))
(PARI) { for (n=1, 1000, a=if (n>1 && n%2, 2*n, n); write("b066043.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 08 2009

Crossrefs

Sequence in context: A334205 A227389 A015906 * A238642 A145019 A066678

Adjacent sequences: A066040 A066041 A066042 * A066044 A066045 A066046

Keyword

easy,nonn

Author

George E. Antoniou, Nov 30 2001

Status

approved