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

2, 3, 5, 7, 29, 349, 359, 1091, 3079, 8423, 64579, 64609, 64709, 481043, 481067, 3524317, 3524387, 9559799, 9560009, 9560039, 25874767, 70115921, 189962009, 189962189, 189964241, 189964259, 189964331, 189964367, 189968741, 189968921

Offset: 1

Author

Patrick De Geest, Nov 15 1999

Keywords

• nonn

Examples

			29 is the tenth prime and 29 == -1 mod 10, so 29 is in the sequence.
31 is the eleventh prime but 31 == 9 mod 11, so 31 is not in the sequence.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..108 (first 53 terms from Charles R Greathouse IV)

Crossrefs

Cf. A045924, A023143, A048891.

Subsequence of A162567.

Programs

Mathematica

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 *)
Select[Prime[Range[5000]], Divisible[# + 1, PrimePi[#]] &] (* Alonso del Arte, May 12 2017 *)
Select[Table[{n,Prime[n]},{n,1056*10^4}],Mod[#[[2]],#[[1]]]==#[[1]]-1&][[All,2]] (* Harvey P. Dale, Oct 29 2022 *)

PARI

lista(nn) = forprime(p=2, nn, if (Mod(p,primepi(p)) + 1 == 0, print1(p, ", "))) \\ Michel Marcus, Jan 09 2015

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

Formula

a(n) = prime(A045924(n)). - Michel Marcus, Jan 09 2015