A317687 - OEIS

%I #17 May 18 2019 07:46:06

%S 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 35,37,27,21,33,39,42,30,18,36,45,51,57,24,40,32,49,47,34,38,43,53,55,

%U 41,67,61,83,79,65,63,81,111,105,87,75,69,59,85,77,115

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

%C The 2-smooth variant of this sequence, say b, satisfies b(n) = A001045(n+1) for any n > 0.

%H Rémy Sigrist, <a href="/A317687/b317687.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A317687/a317687.png">Scatterplot of the first 6500000 terms</a>

%H Rémy Sigrist, <a href="/A317687/a317687.txt">C++ program for A317687</a>

%e The first terms, alongside a(n) + a(n+1), are:

%e   n   a(n)    a(n) + a(n+1)

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

%e    1     1    3

%e    2     2    2 * 3

%e    3     4    3^2

%e    4     5    2^3

%e    5     3    3^2

%e    6     6    2^4

%e    7    10    2 * 3^2

%e    8     8    2^3 * 3

%e    9    16    3^3

%e   10    11    2 * 3^2

%t 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 (C++) See Links section.

%Y Cf. A001045, A003586.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Aug 04 2018