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

Author

George E. Antoniou, Nov 30 2001

Keywords

• easy
• nonn

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

Examples

			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).
		

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).

Programs

Mathematica

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

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

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)