A241291 Decimal expansion of 2^(2^(2^(2^(2^2)))) = 2^^6.

2, 1, 2, 0, 0, 3, 8, 7, 2, 8, 8, 0, 8, 2, 1, 1, 9, 8, 4, 8, 8, 5, 1, 6, 4, 6, 9, 1, 6, 6, 2, 2, 7, 4, 6, 3, 0, 8, 3, 5, 6, 5, 4, 2, 3, 0, 6, 7, 5, 3, 7, 2, 4, 8, 3, 6, 2, 5, 9, 5, 1, 7, 5, 2, 3, 5, 4, 4, 1, 4, 5, 6, 5, 5, 6, 1, 1, 6, 1, 0, 4, 0, 7, 0, 8, 7, 7, 1, 0, 0, 8, 8, 0, 6, 9, 3, 2, 2, 1, 3, 9, 7, 3, 7, 3

Offset: 1

Author

Robert Munafo and Robert G. Wilson v, Apr 18 2014

Keywords

• nonn
• cons
• fini

Comments

The offset is 1 because the true offset would be 6.0312260626165015 * 10^19727, which is too large to be represented properly in the OEIS.

2^0 = 1, 2^1 = 2, 2^2 = 4,

2^2^2 = 2^^3 = (2^2)^2 = 16,

2^2^2^2 = 2^^4 = (((2^2)^2)^2)^2 = 65536,

2^(2^(2^(2^2))) = 2^^5 = (((((((((((((((2^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2 =

2003529930406846464979072351560255750447825475569751419265016973710894059556311453089506130880933348...(19529 digits)...9087575630505718260979581044520267611188489786293085833548068862693010305614986891826277507437428736.

Examples

			2120038728808211984885164691662274630835654230675372483625951752354414565561161040708771008806932213...(10^(6.0312260626165015 * 10^19727))...9087575630505718260979581044520267611188489786293085833548068862693010305614986891826277507437428736.
The above example line shows the first one hundred decimal digits and the last one hundred digits with the number of unrepresented digits in parentheses.
		

Links

• Robert P. Munafo, Sequence A094358, 2^^N = 1 mod N.
• Robert P. Munafo, Hyper4 Iterated Exponential Function.

Crossrefs

Cf. A014221, A085667, A202955, A054382, A014221, A241292, A241293, A241294, A241295, A241296, A241297, A241298, A241299, A243913.

Programs

Mathematica

nbrdgt = 105; f[base_, exp_] := RealDigits[ 10^FractionalPart[ N[ exp*Log10[ base], nbrdgt + Floor[ Log10[ exp]] + 2]], 10, nbrdgt][[1]]; f[2, 2^2^2^2^2]

Formula

Equals 2^2^2^2^2^2 = 2^^6.

Extensions

Keyword: fini added by Jianing Song, Sep 18 2019