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A317687 Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms is 3-smooth (A003586).

%I A317687 #17 May 18 2019 07:46:06
%S A317687 1,2,4,5,3,6,10,8,16,11,7,9,15,12,20,28,26,22,14,13,19,17,31,23,25,29,
%T A317687 35,37,27,21,33,39,42,30,18,36,45,51,57,24,40,32,49,47,34,38,43,53,55,
%U A317687 41,67,61,83,79,65,63,81,111,105,87,75,69,59,85,77,115
%N A317687 Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms is 3-smooth (A003586).
%C A317687 The 2-smooth variant of this sequence, say b, satisfies b(n) = A001045(n+1) for any n > 0.
%H A317687 Rémy Sigrist, <a href="/A317687/b317687.txt">Table of n, a(n) for n = 1..10000</a>
%H A317687 Rémy Sigrist, <a href="/A317687/a317687.png">Scatterplot of the first 6500000 terms</a>
%H A317687 Rémy Sigrist, <a href="/A317687/a317687.txt">C++ program for A317687</a>
%e A317687 The first terms, alongside a(n) + a(n+1), are:
%e A317687   n   a(n)    a(n) + a(n+1)
%e A317687   --  ----    -------------
%e A317687    1     1    3
%e A317687    2     2    2 * 3
%e A317687    3     4    3^2
%e A317687    4     5    2^3
%e A317687    5     3    3^2
%e A317687    6     6    2^4
%e A317687    7    10    2 * 3^2
%e A317687    8     8    2^3 * 3
%e A317687    9    16    3^3
%e A317687   10    11    2 * 3^2
%t A317687 Nest[Append[#, Block[{k = 2}, While[Nand[FreeQ[#, k], SubsetQ[{2, 3}, FactorInteger[k + #[[-1]] ][[All, 1]]]], k++]; k]] &, {1}, 65] (* _Michael De Vlieger_, Aug 05 2018 *)
%o A317687 (C++) See Links section.
%Y A317687 Cf. A001045, A003586.
%K A317687 nonn
%O A317687 1,2
%A A317687 _Rémy Sigrist_, Aug 04 2018