A358085 - OEIS

%I #17 Nov 03 2022 10:06:43

%S 1,1,1,2,1,2,3,4,1,2,3,5,4,6,7,8,1,2,3,5,9,4,6,7,10,11,8,12,13,14,15,

%T 16,1,2,3,5,9,17,4,6,7,10,11,18,19,8,12,13,14,15,20,22,23,24,16,21,25,

%U 26,27,28,29,30,31,32

%N Inventory of positions ordered by binary lengths of terms, as an irregular table; the first row contains 1, subsequent rows contains the 1-based positions of terms with binary length 1, followed by positions of terms with binary length 2, 3, etc. in prior rows flattened.

%C The n-th row contains A011782(n-1) terms, and is a permutation of 1..A011782(n-1).

%H Rémy Sigrist, <a href="/A358085/b358085.txt">Table of n, a(n) for n = 1..8192</a>

%H Rémy Sigrist, <a href="/A358085/a358085.gp.txt">PARI program</a>

%H Rémy Sigrist, <a href="/A358085/a358085.png">Scatterplot of the first 2^20 terms</a>

%e Table begins:

%e     1,

%e     1,

%e     1, 2,

%e     1, 2, 3, 4,

%e     1, 2, 3, 5, 4, 6, 7, 8,

%e     1, 2, 3, 5, 9, 4, 6, 7, 10, 11, 8, 12, 13, 14, 15, 16,

%e     ...

%e For n = 6:

%e - the terms in rows 1..5 are: 1, 1, 1, 2, 1, 2, 3, 4, 1, 2, 3, 5, 4, 6, 7, 8,

%e - terms with binary length 1 are at positions: 1, 2, 3, 5, 9,

%e - terms with binary length 2 are at positions: 4, 6, 7, 10, 11,

%e - terms with binary length 3 are at positions: 8, 12, 13, 14, 15,

%e - terms with binary length 4 are at positions: 16,

%e - so row 6 is: 1, 2, 3, 5, 9, 4, 6, 7, 10, 11, 8, 12, 13, 14, 15, 16.

%o (PARI) See Links section.

%Y Cf. A011782, A070939, A342585, A356784, A358121.

%K nonn,base,tabf

%O 1,4

%A _Rémy Sigrist_, Oct 30 2022