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%I #5 Jul 16 2022 01:30:50
%S 2,5,7,19,127,911,7331,167149,387749,17153317,432383657,10459192927
%N a(1) = 2. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).
%C Is this an increasing sequence or does it enter a cycle?
%o (PARI) seq(start, terms) = my(x=start, i=1); print1(start, ", "); while(1, forprime(q=1, , if(Mod(q, x^2)^(x-1)==1, print1(q, ", "); x=q; i++; if(i >= terms, break({2}), break))))
%o seq(2, 20) \\ Print initial 20 terms of sequence
%Y Row n = 1 of A249162.
%Y Cf. A355598, A355599, A355600, A355601, A355602.
%K nonn,hard,more
%O 1,1
%A _Felix Fröhlich_, Jul 09 2022