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

1,2

Comments

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

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

Example

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

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 *)

Prog

(C++) See Links section.

Crossrefs

Cf. A001045, A003586.

Sequence in context: A060120 A065183 A119791 * A026257 A357986 A099520

Adjacent sequences: A317684 A317685 A317686 * A317688 A317689 A317690

Keyword

nonn

Author

Rémy Sigrist, Aug 04 2018

Status

approved