A042974 n 1's followed by a 2.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• cons

Comments

The number 1.21121112... is irrational. - Robert G. Wilson v, Jul 05 2000

Fixed point of the following mapping w. Suppose x(n) takes values in {1,2} and w(n)=[x(1),x(2),...,x(n)]. Next define w(n+1)=[x(1),x(2),...,x(n),x(n-1)] if x(n)=1 and w(n+1)=[x(1),x(2),...,x(n),x(n-1),x(n-1)] if x(n)=2. Then taking x(1)=1 and x(2)=2 we get w(infinity)=A042974 (i.e., x(n)=A042974(n)). - Benoit Cloitre, Jan 11 2013

Examples

			1.211211121111211111211111121111111211111111211111111121111111111211111...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• C. V. Eynden, Problem 10439. An irrational mimic of 1/9, Amer. Math. Monthly, 104 (1997), 873.
• G. Xiao, Contfrac
• Index entries for continued fractions for constants

Crossrefs

Cf. A042975, A056030 (continued fraction).

Programs

Haskell

a042974 n = a042974_list !! (n-1)
a042974_list =  1 : 2 :
   concat (zipWith replicate (tail a042974_list) a042974_list)
-- Reinhard Zumkeller, Dec 08 2011

Mathematica

Table[PadLeft[{2},n,1],{n,2,20}]//Flatten (* Harvey P. Dale, Sep 11 2019 *)

PARI

{a(n) = 1 + issquare(9 + 8*n)}; /* Michael Somos, Jan 12 2000 */

PARI

{ default(realprecision, 20080); x=0; for (n=1, 20000, x=10*x + 1 + issquare(9+8*n)); x/=10^19999; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b042974.txt", n, " ", d)); } \\ Harry J. Smith, May 08 2009

PARI

sum(k=1,sqrtint(8*default(realprecision)+9),10^-(2*k-1)^2, 1/9.) \\ Charles R Greathouse IV, Feb 05 2025