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

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, 35, 37, 27, 21, 33, 39, 42, 30, 18, 36, 45, 51, 57, 24, 40, 32, 49, 47, 34, 38, 43, 53, 55, 41, 67, 61, 83, 79, 65, 63, 81, 111, 105, 87, 75, 69, 59, 85, 77, 115

Offset: 1

Author

Rémy Sigrist, Aug 04 2018

Keywords

• nonn

Comments

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

Examples

			The first terms, alongside a(n) + a(n+1), are:
  n   a(n)    a(n) + a(n+1)
  --  ----    -------------
   1     1    3
   2     2    2 * 3
   3     4    3^2
   4     5    2^3
   5     3    3^2
   6     6    2^4
   7    10    2 * 3^2
   8     8    2^3 * 3
   9    16    3^3
  10    11    2 * 3^2
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Scatterplot of the first 6500000 terms
• Rémy Sigrist, C++ program for A317687

Crossrefs

Cf. A001045, A003586.

Programs

Mathematica

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 *)