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A374155 a(n) is the least prime that is a quadratic residue modulo prime(n). First column of A373751.

%I A374155 #13 Jun 29 2024 11:22:00
%S A374155 2,3,5,2,3,3,2,5,2,5,2,3,2,11,2,7,3,3,17,2,2,2,3,2,2,5,2,3,3,2,2,3,2,
%T A374155 5,5,2,3,41,2,13,3,3,2,2,7,2,5,2,3,3,2,2,2,3,2,2,5,2,3,2,7,17,7,2,2,7,
%U A374155 5,2,3,3,2,2,2,3,5,2,5,3,2,2,3,3,2,2,2
%N A374155 a(n) is the least prime that is a quadratic residue modulo prime(n). First column of A373751.
%e A374155 a(38) = 41 because row 38 of A373751 starts 41, 43, 47, ..., which are the primes that are quadratic residues modulo 163.
%p A374155 a := proc(n) local a, p; a := 1; p := ithprime(n); while true do a := a + 1;
%p A374155 if NumberTheory:-QuadraticResidue(a, p) = 1 and isprime(a) then return a fi od end: seq(a(n), n = 1..85);
%o A374155 (PARI) a(n) = my(p=prime(n), q=2); while (!issquare(Mod(q, p)), q=nextprime(q+1)); q; \\ _Michel Marcus_, Jun 29 2024
%Y A374155 Variant: A306530 (differs in the first 3 values).
%Y A374155 Cf. A373751.
%K A374155 nonn
%O A374155 1,1
%A A374155 _Peter Luschny_, Jun 29 2024