A338141 Let R_1 = {1, 2, ...}; for any n > 0, let r_n be the colexicographically earliest finite subset of R_n summing to a prime number, say p; a(n) = p and R_{n+1} = R_n \ r_n.

2, 3, 5, 5, 7, 17, 11, 13, 31, 17, 19, 47, 23, 41, 47, 29, 31, 73, 59, 37, 67, 41, 43, 71, 47, 79, 83, 53, 89, 131, 59, 61, 103, 107, 67, 113, 71, 73, 173, 131, 79, 127, 83, 137, 149, 89, 149, 149, 163, 97, 163, 101, 103, 241, 107, 109, 257, 113, 191, 197, 179

Offset

1,1

Comments

In other words, we partition the natural numbers into finite subsets summing to prime numbers.

Every prime number appears at least once in the sequence.

See A338240 for the corresponding {r_n}.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored scatterplot of the first 100000 terms (where the color is function of the number of elements of r_n)

Rémy Sigrist, PARI program for A338141

Wikipedia, Colexicographic order

Example

The first terms, alongside the corresponding sets r_n, are:
  n   a(n)  r_n
  --  ----  ------------
   1     2  {2}
   2     3  {3}
   3     5  {1, 4}
   4     5  {5}
   5     7  {7}
   6    17  {8, 9}
   7    11  {11}
   8    13  {13}
   9    31  {6, 10, 15}
  10    17  {17}
  11    19  {19}
  12    47  {12, 14, 21}
  13    23  {23}
  14    41  {16, 25}
  15    47  {20, 27}

Prog

(PARI) See Links section.

Crossrefs

Cf. A338240.

Sequence in context: A302445 A094749 A096539 * A067364 A090547 A087308

Adjacent sequences: A338138 A338139 A338140 * A338142 A338143 A338144

Keyword

nonn

Author

Rémy Sigrist, Oct 12 2020

Status

approved