A305464 Largest 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.

5, 13, 41, 101, 277, 491, 0, 577, 1181, 1409, 1201, 0, 2801, 2851, 1217, 4013, 3061, 1901, 4241, 9619, 10781, 6947, 7681, 8501, 11597, 14149, 18089, 10847

Offset: 2

Author

Jeremy F. Alm, Jun 01 2018

Keywords

• nonn
• more

Comments

a(n) <= n^4 + 5 (cf. Alm, 2017). There cannot be arbitrarily large multiplicative-coset Ramsey algebras in a fixed number of colors.

a(n) < A294676(n).

Links

• 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.)

Crossrefs

Cf. A263308, A294676.