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A382374 Lexicographically earliest sequence of distinct positive integers such that the number of prime factors counted with multiplicity of adjacent terms differ exactly by one.

%I A382374 #11 Mar 26 2025 18:19:42
%S A382374 1,2,4,3,6,5,9,7,10,8,14,11,15,12,16,18,21,13,22,17,25,19,26,20,24,27,
%T A382374 33,23,34,28,35,29,38,30,36,32,40,42,39,31,46,37,49,41,51,43,55,44,54,
%U A382374 45,56,48,60,50,57,47,58,52,62,53,65,59,69,61,74,63,77
%N A382374 Lexicographically earliest sequence of distinct positive integers such that the number of prime factors counted with multiplicity of adjacent terms differ exactly by one.
%C A382374 All powers of 2 appear in the sequence (we can use similar arguments as for A382357).
%C A382374 Conjecture: this sequence is a permutation of the positive integers.
%H A382374 Rémy Sigrist, <a href="/A382374/b382374.txt">Table of n, a(n) for n = 1..10000</a>
%H A382374 Rémy Sigrist, <a href="/A382374/a382374.gp.txt">PARI program</a>
%e A382374 The initial terms are:
%e A382374   n   a(n)  A001222(a(n))
%e A382374   --  ----  -------------
%e A382374    1     1              0
%e A382374    2     2              1
%e A382374    3     4              2
%e A382374    4     3              1
%e A382374    5     6              2
%e A382374    6     5              1
%e A382374    7     9              2
%e A382374    8     7              1
%e A382374    9    10              2
%e A382374   10     8              3
%e A382374   11    14              2
%e A382374   12    11              1
%e A382374   13    15              2
%e A382374   14    12              3
%e A382374   15    16              4
%o A382374 (PARI) \\ See Links section.
%Y A382374 Cf. A001222, A382229, A382357, A382375, A382376.
%K A382374 nonn
%O A382374 1,2
%A A382374 _Rémy Sigrist_, Mar 23 2025