A141044 Two 2's followed by all 1's.

2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,1

Comments

Essentially the same as the "all ones" sequence A000012. - M. F. Hasler, May 30 2020

Decimal expansion of 199/900 = .2211111111111111... - Bernard Schott, May 30 2020

Continued fraction expansion of (7 - sqrt(5))/2 = A079585. - Elmo R. Oliveira, Sep 22 2025

Links

Table of n, a(n) for n=0..104.

Wikipedia, Hyperoperation

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

Formula

G.f.: 2*(1+x)-x^2/(x-1). - R. J. Mathar, May 10 2001

a(n) = H_n(1, 1), where H_n is the n-th hyperoperator (cf. A054871). - Natan Arie Consigli, Feb 26 2015

a(n) = A000012(n) for all n > 1. - M. F. Hasler, May 30 2020

E.g.f.: exp(x) + 1 + x. - Elmo R. Oliveira, Sep 22 2025

Mathematica

PadRight[{2, 2}, 120, 1] (* Harvey P. Dale, Jan 02 2022 *)

Prog

(PARI) a(n)=if(n>1, 1, 2) \\ Charles R Greathouse IV, Oct 07 2015
(PARI) apply( {A141044(n)=(n<2)+1}, [0..90]) \\ M. F. Hasler, May 30 2020

Crossrefs

Cf. A000012, A054871, A079585, A005126 (binomial transform).

Sequence in context: A211312 A085978 A380759 * A064284 A371807 A370975

Adjacent sequences: A141041 A141042 A141043 * A141045 A141046 A141047

Keyword

nonn,easy

Author

Paul Curtz, Jul 31 2008

Extensions

Edited by N. J. A. Sloane, Mar 03 2010

Status

approved