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A375579 Lexicographically earliest sequence of distinct positive integers such that the products of two consecutive terms belong to A055932.

%I A375579 #13 Aug 26 2024 13:13:30
%S A375579 1,2,3,4,6,5,12,8,9,10,15,14,30,7,60,16,18,20,21,40,24,25,36,27,32,45,
%T A375579 28,75,42,35,48,50,54,64,72,70,33,140,63,80,81,90,49,120,56,105,22,
%U A375579 210,11,420,44,315,66,175,84,55,126,100,96,108,125,144,128,135
%N A375579 Lexicographically earliest sequence of distinct positive integers such that the products of two consecutive terms belong to A055932.
%C A375579 a(n+1) is a multiple of A083720(a(n)).
%C A375579 This sequence has similarities with A175343; here we consider prime factors of consecutive terms, there ones in binary expansions of consecutive terms.
%H A375579 Rémy Sigrist, <a href="/A375579/b375579.txt">Table of n, a(n) for n = 1..10000</a>
%H A375579 Rémy Sigrist, <a href="/A375579/a375579.gp.txt">PARI program</a>
%e A375579 The first terms, alongside their prime factors, are:
%e A375579   n   a(n)  2  3  5  7
%e A375579   --  ----  -  -  -  -
%e A375579    1     1
%e A375579    2     2  X
%e A375579    3     3     X
%e A375579    4     4  X
%e A375579    5     6  X  X
%e A375579    6     5        X
%e A375579    7    12  X  X
%e A375579    8     8  X
%e A375579    9     9     X
%e A375579   10    10  X     X
%e A375579   11    15     X  X
%e A375579   12    14  X        X
%o A375579 (PARI) \\ See Links section.
%Y A375579 Cf. A055932, A083720, A175343, A375281, A375615.
%K A375579 nonn
%O A375579 1,2
%A A375579 _Rémy Sigrist_, Aug 19 2024