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A343908 a(n) is the least prime == 4 (mod prime(n)).

%I A343908 #27 May 31 2021 19:27:09
%S A343908 2,7,19,11,37,17,89,23,73,149,97,41,127,47,239,163,181,431,71,359,223,
%T A343908 83,419,271,101,307,107,967,113,569,131,397,1237,421,2239,457,1103,
%U A343908 167,839,523,541,547,577,197,1777,601,1481,227,3863,233,3499,2633,727,757,1289,1319,811,1901,281,1409
%N A343908 a(n) is the least prime == 4 (mod prime(n)).
%H A343908 Alois P. Heinz, <a href="/A343908/b343908.txt">Table of n, a(n) for n = 1..10000</a>
%e A343908 a(3) = 19 because 19 is the least prime == 4 (mod prime(3)).
%e A343908 a(4) = 11 because 11 is the least prime == 4 (mod prime(4)).
%p A343908 a:= proc(n) local q, p; p:= ithprime(n); q:= p;
%p A343908       do if irem(q-4, p)=0 then break fi;
%p A343908          q:= nextprime(q);
%p A343908       od; q
%p A343908     end:
%p A343908 seq(a(n), n=1..60);  # _Alois P. Heinz_, May 03 2021
%t A343908 s = {}; p = 5; Do[q = p + 2; While[Mod[q, p] != 4, q = NextPrime[q]]; AppendTo[s, q]; p = NextPrime[p], {100}]; s
%o A343908 (PARI) a(n) = my(p=prime(n)); forprime(q=2,, if (Mod(q, p) == 4, return(q))); \\ _Michel Marcus_, May 03 2021
%Y A343908 Cf. A000040, A023200 (primes p such that p+4 is also prime), A034694, A035095, A279756.
%K A343908 nonn
%O A343908 1,1
%A A343908 _Zak Seidov_, May 03 2021