A097374 -id:A097374 - cp's OEIS frontend

A381538 Numbers of the form m^(m^k).

1, 4, 16, 27, 256, 3125, 19683, 46656, 65536, 823543, 16777216, 387420489, 4294967296, 10000000000, 285311670611, 7625597484987, 8916100448256, 302875106592253, 11112006825558016, 298023223876953125, 437893890380859375, 18446744073709551616

Offset: 1

Charles L. Hohn, Feb 26 2025

nonn

			27 = 3^(3^1) -> a(4).
256 = 2^(2^3) = 4^(4^1) -> a(5).

Subsequence of A001597; supersequence of A000312 (apart from initial term), A097374, and A257309 (apart from initial term).

Subset of A380760 for a(n)>=16, and of A067688 for prime m.

upto(limit)=my(L=List([1])); for(m=2, oo, my(t=logint(limit,m)); if(tAndrew Howroyd, Feb 26 2025

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

Original entry on oeis.org

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

Natan Arie Consigli, Jan 19 2016

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

			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.

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

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

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)

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A381538 Numbers of the form m^(m^k).

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

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