A255176 a(n) = H_n(2,2) where H_n is the n-th hyperoperator.

3, 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, 4, 4, 4, 4

Offset

0,1

Comments

See A054871 for definitions and key links.

Also, decimal expansion of 31/90. - Bruno Berselli, Mar 18 2015

Essentially the same as A010709, A040002, A113311, A123932, and A151798. - R. J. Mathar, Mar 20 2015

Remainder of the Euclidean division when 10^(10^n) is divided by 7 (proof by induction for n >= 1) [see reference Julien Freslon and Jérôme Poineau]; example: 10^(10^1) = 1428571428 * 7 + 4. - Bernard Schott, Aug 28 2020

Continued fraction expansion of 1 + sqrt(5) = A134945. - Elmo R. Oliveira, Sep 22 2025

References

Julien Freslon and Jérôme Poineau, Les 100 exercices-types de mathématiques: MPSI/PCSI/PTSI, EdiScience, 2007, Exercice 11.2, page 242.

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.: (3 + x)/(1 - x). - Bruno Berselli, Mar 18 2015

a(n) = 10^(10^n) mod 7. - Bernard Schott, Aug 28 2020

E.g.f.: 4*exp(x) - 1. - Elmo R. Oliveira, Sep 22 2025

Example

a(0) = H_0(2,2) = 2+1 = 3.
a(1) = H_1(2,2) = 2+2 = 4.
a(2) = H_2(2,2) = 2*2 = 4.
a(3) = H_3(2,2) = 2^2 = 4.
a(n) = H_n(2,2) = H_{n-1}(2,H_n(2,1)) = H_{n-1}(2,2) = 4, for n>1.
As a constant: 0.34444444444444444444444444444444444444444444444444...

Mathematica

PadRight[{3}, 100, 4] (* Paolo Xausa, Apr 21 2026 *)

Crossrefs

Cf. A010709, A040000, A040002, A054871, A113311, A123932, A151798, A157532.

Cf. A134945.

Sequence in context: A280356 A018244 A113311 * A288177 A349992 A064042

Adjacent sequences: A255173 A255174 A255175 * A255177 A255178 A255179

Keyword

nonn,easy,cons

Author

Natan Arie Consigli, Feb 25 2015

Extensions

Edited by Danny Rorabaugh, Oct 20 2015

Status

approved