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A386932 Lexicographically earliest sequence of distinct positive integers that can be partitioned into runs of integers without common bits, the n-th such run having a(n) terms.

%I A386932 #9 Aug 15 2025 09:11:18
%S A386932 1,2,4,3,8,16,32,5,10,48,6,9,64,128,256,512,1024,2048,7,24,96,384,
%T A386932 1536,4096,8192,16384,32768,65536,131072,262144,524288,1048576,
%U A386932 2097152,4194304,11,20,160,320,2560,5120,24576,98304,393216,1572864,6291456,8388608
%N A386932 Lexicographically earliest sequence of distinct positive integers that can be partitioned into runs of integers without common bits, the n-th such run having a(n) terms.
%C A386932 This sequence is a permutation of the positive integers as each run starts with the least integer not yet in the sequence.
%C A386932 The powers of two appear in natural order.
%H A386932 Rémy Sigrist, <a href="/A386932/b386932.txt">Table of n, a(n) for n = 1..6223</a>
%H A386932 Rémy Sigrist, <a href="/A386932/a386932.png">Logarithmic scatterplot of the first 10319 terms</a> (where red pixels correspond to powers of 2)
%H A386932 Rémy Sigrist, <a href="/A386932/a386932.gp.txt">PARI program</a>
%H A386932 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A386932 The first terms and runs are:
%e A386932   n  a(n)  n-th run
%e A386932   -  ----  -----------------------------------
%e A386932   1     1  1
%e A386932   2     2  2, 4
%e A386932   3     4  3, 8, 16, 32
%e A386932   4     3  5, 10, 48
%e A386932   5     8  6, 9, 64, 128, 256, 512, 1024, 2048
%o A386932 (PARI) \\ See Links section.
%Y A386932 See A385661 for a similar sequence.
%Y A386932 Cf. A358875, A387024 (inverse).
%K A386932 nonn,tabf,base
%O A386932 1,2
%A A386932 _Rémy Sigrist_, Aug 09 2025