A364874 A packing coloring for the one-way infinite path using only the first 8 prime numbers.

2, 3, 5, 2, 7, 3, 2, 11, 5, 2, 3, 13, 2, 7, 3, 2, 5, 17, 2, 3, 11, 2, 5, 3, 2, 7, 13, 2, 3, 5, 2, 19, 3, 2, 7, 5, 2, 3, 11, 2, 13, 3, 2, 5, 7, 2, 3, 17, 2, 5, 3, 2, 7, 11, 2, 3, 5, 2, 13, 3, 2, 7, 5, 2, 3, 11, 2, 17, 3, 2, 5, 7, 2, 3, 13, 2, 5, 3, 2, 7, 11, 2, 3, 5, 2, 17, 3, 2

Offset

1,1

Comments

a(1)=2; for n > 1, a(n) is the smallest number in the set S = {2,3,5,7,11,13,17,19}, subject to the constraint that for m < n, if a(m) = a(n) = s_i, n-m > s_i.

Observations:

The sequence is eventually periodic after the 129th term, with the repetend being the last 54 terms provided above. The repetend itself, repeated periodically, is also a packing coloring for the one-way and two-way infinite paths using this set S.

The chromatic number for packing the two-way infinite path with primes may be 8.

Links

Table of n, a(n) for n=1..88.

Crossrefs

Sequence in context: A066949 A073481 A178094 * A122556 A175723 A084346

Adjacent sequences: A364871 A364872 A364873 * A364875 A364876 A364877

Keyword

easy,nonn

Author

Kenneth A. Dennison, Aug 11 2023

Status

approved