A375374 - OEIS

A375374

Let X be the sequence of power towers built of 2's and 3's, sorted first by their height and then colexicographically: 2, 3, 2^2, 3^2, 2^3, 3^3, 2^2^2, 3^2^2, etc. Sequence gives the permutation of indices which reorders X by magnitude.

1, 2, 3, 5, 4, 7, 6, 8, 11, 9, 12, 10, 15, 16, 13, 14, 17, 18, 23, 24, 19, 20, 25, 26, 21, 22, 31, 32, 33, 34, 27, 28, 29, 30, 35, 36, 37, 38, 47, 48, 49, 50, 39, 40, 41, 42, 51, 52, 53, 54, 43, 44, 45, 46, 63, 64, 65, 66, 67, 68, 69, 70, 55, 56, 57, 58, 59, 60

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OFFSET

1,2

COMMENTS

The terms are less dispersed here compared to A185969, because colex order is more correlated to the magnitude of the power tower than lex order is, i.e., we often get a smaller value of the power tower by putting the small numbers high up in the tower. Specifically, the only integers x, y >= 2 for which x < y and x^y < y^x is x = 2, y = 3.

LINKS

Table of n, a(n) for n=1..68.

Index entries for sequences that are permutations of the natural numbers.

FORMULA

a(2*n-1) = 2*a(n-1)+1 and a(2*n) = a(2*n-1)+1 for n >= 7.

a(n) = A081241(A185969(n)).

CROSSREFS

3rd row of A375376.

Cf. A081241, A185969 (lexicographic instead of colexicographic order), A375375 (inverse permutation).

Sequence in context: A342265 A375375 A230086 * A333404 A227082 A227142

Adjacent sequences: A375371 A375372 A375373 * A375375 A375376 A375377

KEYWORD

nonn

AUTHOR

Pontus von Brömssen, Aug 13 2024

STATUS

approved