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A263308
Smallest prime modulus p such that there exists a multiplicative-coset Ramsey algebra in n colors over Z/pZ, or 0 if no such prime exists.
4
2, 5, 13, 41, 71, 97, 491, 0, 523, 1181, 947, 769, 0, 1709, 1291, 1217, 4013, 2521, 1901, 2801, 1933, 3257, 3221, 4129, 3701, 4889, 5563, 8849, 6323, 5521, 6263, 5441, 8779, 7481, 7841, 10009, 13469, 12161, 8971, 14561, 13367, 19993, 14621, 12497, 14401, 14537, 20117, 18913, 22541, 22901, 19687, 29537
OFFSET
1,1
COMMENTS
a(8) = 0 means there is NO prime satisfying the condition. a(n) is known for 1 <= n <= 2000.
LINKS
Jeremy F. Alm and Jacob Manske, Sum-free cyclic multi-bases and constructions of Ramsey algebras, Discrete Applied Mathematics, (180), Jan 10 2015, pp. 204-212. (arXiv:1307.0889 [math.CO], 2013-2014.)
Jeremy F. Alm, 401 and beyond: improved bounds and algorithms for the Ramsey algebra search, Journal of Integer Sequences, Vol. 20 (2017), Article 17.8.4. (Also here: arXiv:1609.01817 [math.NT], 2016.)
Jeremy F. Alm, Python program.
Tomasz Kowalski, Representability of Ramsey Relation Algebras, Algebra Universalis, Volume 74, Issue 3-4, November 2015, pp. 265-275.
PROG
(Python) # See Links section.
CROSSREFS
Sequence in context: A149867 A062704 A274909 * A288388 A339224 A247981
KEYWORD
nonn
AUTHOR
Jeremy F. Alm, Oct 13 2015
EXTENSIONS
More terms from Jeremy F. Alm, Sep 05 2016
STATUS
approved