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%I #15 Jan 18 2025 09:34:47
%S 41,113,229,337,349,433,457,461,557,593,617,653,677,853,857,877,929,
%T 977,997,1021,1129,1153
%N Primes p such that p == 1 (mod 4) and the Paley graph of order p is not alpha-critical.
%C For a prime p with p == 1 (mod 4), the Paley graph P_p is defined to have vertices 0,1,...,p-1, with vertices v,w adjacent if and only if the difference v-w is a quadratic residue mod p. A graph is alpha-critical if the removal of any edge increases the independence number of the resulting subgraph.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Paley_graph">Paley graph</a>.
%e The Paley graph P_5 is the cycle on 5-vertices. P_5 is alpha-critical. So p=5 is not a term.
%e The first non-alpha-critical Paley graph is P_41 and thus the first term is 41.
%K nonn,more
%O 1,1
%A _Craig Eric Larson_, Dec 28 2024