A267649 a(0) = a(1) = 2 then a(n) = 4 for n>=2.

2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 0

Author

Natan Arie Consigli, Jan 19 2016

Keywords

• nonn
• easy
• cons
• less

Comments

Decimal expansion of 101/450.

Also list of smallest n-composites.

A hyperoperator aggregation b[n]c is n-composite if b,c are positive non-right-identity elements.

The identity elements are:

Hyper-0 (zeration): none.

Hyper-1 (addition): 0.

Hyper-2 (multiplication): 1.

Hyper-3 (exponentiation): 1.

Hyper-n (n>2): 1.

For more information on hyperoperations see A054871.

Essentially the same as A255176, A151798, A123932, A113311, A040002 and A010709. - R. J. Mathar, May 25 2023

Continued fraction expansion of 2 + sqrt(1/5) = 2 + sqrt(5)/5. - Elmo R. Oliveira, Aug 06 2024

Examples

			a(0) = 2 because 1 is the smallest non-identity element in zeration and 1[0]1=2;
a(1) = 2 because 1 is the smallest non-identity element in addition and 1[1]1=2;
a(2) = 4 because 2 is the smallest non-identity element in multiplication and 2[2]2=4;
a(3) = 4 because 2 is the smallest non-identity element in exponentiation and 2[2]2=4;
a(4) = 4 because 2 is the smallest non-identity element in titration and 2[2]2=4;
Etc.
		

Links

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

Crossrefs

Cf. A000027 (1-composites), A002808 (composites), A267647 (3-composites), A097374 (4-composites).

Formula

a(n) = a[n]b where a,b are the positive smallest non-right-identity elements.

From Elmo R. Oliveira, Aug 06 2024: (Start)

G.f.: 4/(1 - x) - 2*(1 + x).

E.g.f.: 4*exp(x) - 2*(1 + x). (End)