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The primes associated with A339174.
1

%I #7 Jan 02 2023 09:01:05

%S 2,3,7,43,3613,65250781,38318979202732621,

%T 8810065002836730577256726488782121,

%U 6131762382982476362788562753503495060507087787406616806191258317645081

%N The primes associated with A339174.

%C a(1)=2; for n > 0, a(n+1) is the first prime of the form k*(a(n) - 1)*a(n) + 1. It exists by Dirichlet's theorem on arithmetic progressions.

%C It is simple to reconstruct a(n) from A339174, which has the more compact representation.

%o (PARI) p=2; k=1; print1(p, ", "); while(1, runningP=k*(p-1)*p+1; if(ispseudoprime(runningP), k=1; p=runningP; print1(p, ", ") , k++))

%Y Cf. A061092, A071580, A339174.

%K nonn

%O 1,1

%A _Jeppe Stig Nielsen_, Dec 27 2022