A128999 Start with an integer (in this case 1). First, add 5 or 6 if the integer is odd or even, respectively. Then divide by 2.

1, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

Author

Adam F. Schwartz (adam_s(AT)mit.edu), May 01 2007

Keywords

• easy
• nonn

Comments

Note that any a(1) <= 5 converges to 5 and any a(1) >= 6 converges to 6.

Decimal expansion of 1211/900. - Elmo R. Oliveira, May 05 2024

Links

• Tanya Khovanova, Arithmetic Progression.
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A085600.

Programs

Mathematica

PadRight[{1, 3, 4}, 100, 5] (* Paolo Xausa, Aug 28 2024 *)

Formula

a(n) = [a(n-1) + b]/d, if a(n) even = [a(n-1) + c]/d, if a(n) odd (starting a(1)=1 with b=5, c=6, d=2).

a(n) = 5 for n >= 4. - R. J. Mathar, Oct 31 2007

G.f.: x*(1+2*x+x^2+x^3)/(1-x). - Elmo R. Oliveira, May 05 2024

Extensions

More terms from R. J. Mathar, Oct 31 2007