The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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
 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 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 17 22:15 EDT 2021. Contains 343992 sequences. (Running on oeis4.)