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

Offset: 1

Author

Pontus von Brömssen, Aug 13 2024

Keywords

• nonn

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

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

Crossrefs

3rd row of A375376.

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

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)).