A375579 - OEIS

%I #13 Aug 26 2024 13:13:30

%S 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 28,75,42,35,48,50,54,64,72,70,33,140,63,80,81,90,49,120,56,105,22,

%U 210,11,420,44,315,66,175,84,55,126,100,96,108,125,144,128,135

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

%C a(n+1) is a multiple of A083720(a(n)).

%C This sequence has similarities with A175343; here we consider prime factors of consecutive terms, there ones in binary expansions of consecutive terms.

%H Rémy Sigrist, <a href="/A375579/b375579.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A375579/a375579.gp.txt">PARI program</a>

%e The first terms, alongside their prime factors, are:

%e   n   a(n)  2  3  5  7

%e   --  ----  -  -  -  -

%e    1     1

%e    2     2  X

%e    3     3     X

%e    4     4  X

%e    5     6  X  X

%e    6     5        X

%e    7    12  X  X

%e    8     8  X

%e    9     9     X

%e   10    10  X     X

%e   11    15     X  X

%e   12    14  X        X

%o (PARI) \\ See Links section.

%Y Cf. A055932, A083720, A175343, A375281, A375615.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Aug 19 2024