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

1,1

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A045924, A023143, A048891.

Subsequence of A162567.

Sequence in context: A082257 A054750 A048404 * A269022 A174536 A054797

Adjacent sequences: A052010 A052011 A052012 * A052014 A052015 A052016

Keyword

nonn

Author

Patrick De Geest, Nov 15 1999

Status

approved