A329111 a(n) = round(b(n)) where b(n) = b(n-1)^(b(n-1)^(1/b(n-1))) and b(1)=2.

2, 3, 4, 7, 14, 24, 37, 54, 73, 95, 119, 145, 172, 201, 232, 264, 297, 332, 368, 405, 442, 481, 521, 562, 604, 647, 690, 735, 780, 826, 872, 919, 967, 1016, 1065, 1115, 1166, 1217, 1268, 1321, 1373, 1427, 1481, 1535, 1590, 1645, 1701, 1758

Offset

1,1

Links

Table of n, a(n) for n=1..48.

Example

a(1) = 2 because round(b(1)) = 2;
a(2) = 3 because round(2^(2^(1/2))) = 3;
a(3) = 4 because round(b(2)^(b(2)^(1/b(2)))) = 4.

Mathematica

Round@ NestList[#^Power[#, 1/#] &, 2, 12] (* Michael De Vlieger, Nov 18 2019 *)

Prog

(JavaScript)
var x = 2;
var g = [];
for (var i = 0; i < 400; i++) {
  x=Math.pow(x, Math.pow(x, 1/x));
  appendItem(g, Math.round(x));
}
console.log(g);

Crossrefs

Cf. A000196.

Sequence in context: A000690 A049876 A049795 * A014251 A290992 A361229

Adjacent sequences: A329108 A329109 A329110 * A329112 A329113 A329114

Keyword

nonn

Author

Sebastian F. Orellana, Nov 05 2019

Status

approved