A185969 Let S be the sequence of power towers built of 2 and 3 sorted by their height and for equal heights - in lexicographic order: 2, 3, 2^2, 2^3, 3^2, 3^3, 2^2^2, 2^2^3 etc. A(n) = the permutation of indexes which reorders S by magnitude.

1, 2, 3, 4, 5, 7, 6, 11, 8, 9, 12, 13, 15, 23, 10, 14, 19, 27, 16, 24, 17, 25, 20, 28, 21, 29, 31, 47, 39, 55, 18, 26, 22, 30, 35, 51, 43, 59, 32, 48, 40, 56, 33, 49, 41, 57, 36, 52, 44, 60, 37, 53, 45, 61, 63, 95, 79, 111, 71, 103, 87, 119, 34, 50, 42, 58, 38

Offset: 1

Author

Vladimir Reshetnikov, Feb 07 2011

Keywords

• nonn
• look

Examples

			a(6) =  7; tower(7)  = 2^2^2 = 2^4 =  16.
a(7) =  6; tower(6)  = 3^3   =        27.
a(8) = 11; tower(11) = 3^2^2 = 3^4 =  81.
a(9) =  8; tower(8)  = 2^2^3 = 2^8 = 256.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..14335
• Vladimir Reshetnikov, 2-3 sequence puzzle, SeqFan list, Mar 18 2015
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A032810, A081241, A248907, A256179, A256231, A375374 (colexicographic instead of lexicographic order).

Formula

a(2*n-1) = A081241(2*A081241(a(n-1))+1) and a(2*n) = A081241(A081241(a(2*n-1))+1) for n >= 7. - Pontus von Brömssen, Aug 10 2024

Extensions

More terms from Alois P. Heinz, Apr 05 2011