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A052013 Primes that are congruent to -1 mod n, where n is the index of the prime.

%I A052013 #31 Oct 29 2022 15:24:37
%S A052013 2,3,5,7,29,349,359,1091,3079,8423,64579,64609,64709,481043,481067,
%T A052013 3524317,3524387,9559799,9560009,9560039,25874767,70115921,189962009,
%U A052013 189962189,189964241,189964259,189964331,189964367,189968741,189968921
%N A052013 Primes that are congruent to -1 mod n, where n is the index of the prime.
%H A052013 Giovanni Resta, <a href="/A052013/b052013.txt">Table of n, a(n) for n = 1..108</a> (first 53 terms from Charles R Greathouse IV)
%F A052013 a(n) = prime(A045924(n)). - _Michel Marcus_, Jan 09 2015
%e A052013 29 is the tenth prime and 29 == -1 mod 10, so 29 is in the sequence.
%e A052013 31 is the eleventh prime but 31 == 9 mod 11, so 31 is not in the sequence.
%t A052013 divbleQ[m_, n_] := Mod[m, n] == 0; A052013 = {}; Do[p = Prime[n]; If[divbleQ[p + 1, n], AppendTo[A052013, p]], {n, 10!}]; A052013 (* _Vladimir Joseph Stephan Orlovsky_, Dec 08 2009 *)
%t A052013 Select[Prime[Range[5000]], Divisible[# + 1, PrimePi[#]] &] (* _Alonso del Arte_, May 12 2017 *)
%t A052013 Select[Table[{n,Prime[n]},{n,1056*10^4}],Mod[#[[2]],#[[1]]]==#[[1]]-1&][[All,2]] (* _Harvey P. Dale_, Oct 29 2022 *)
%o A052013 (PARI) lista(nn) = forprime(p=2, nn, if (Mod(p,primepi(p)) + 1 == 0, print1(p, ", "))) \\ _Michel Marcus_, Jan 09 2015
%o A052013 (PARI) list(lim)=my(v=List(), n, t); forprime(p=2, lim, t=(p+1)/n++; if(denominator(t)==1, listput(v, p))); Vec(v) \\ _Charles R Greathouse IV_, Feb 18 2016
%Y A052013 Cf. A045924, A023143, A048891.
%Y A052013 Subsequence of A162567.
%K A052013 nonn
%O A052013 1,1
%A A052013 _Patrick De Geest_, Nov 15 1999