A162567 -id:A162567 - cp's OEIS frontend

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

Patrick De Geest, Nov 15 1999

nonn

			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.

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

Cf. A045924, A023143, A048891.

Subsequence of A162567.

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 *)

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

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

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

A078931 Numbers k that divide prime(k)+1 or prime(k)-1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 10, 12, 14, 70, 72, 181, 182, 440, 1053, 6458, 6459, 6460, 6461, 6466, 6471, 40087, 40089, 100362, 251712, 251732, 251737, 251742, 637236, 637320, 637334, 637336, 1617173, 4124466, 10553445, 10553455, 10553504, 10553505, 10553547, 10553569

Offset: 1

Benoit Cloitre, Jan 12 2003

nonn

			181 is in the sequence because the 181st prime is 1087, and 1086 is divisible by 181 (although 1088 is not so divisible).

Amiram Eldar, Table of n, a(n) for n = 1..198 (created using the b-files at A023143 and A045924)

Cf. A000720, A023143, A045924, A162567.

ndpQ[n_]:=Module[{p=Prime[n]},Divisible[p-1,n]||Divisible[p+1,n]]; Select[Range[100000],ndpQ]  (* Harvey P. Dale, Apr 03 2011 *)

Equals A023143 union A045924.

a(n) = A000720(A162567(n)). - Alois P. Heinz, Feb 20 2023

Corrected and example added by Harvey P. Dale, Apr 03 2011

Extended with terms from A023143 and A045924 by Michel Marcus, Nov 30 2013

A360789 Least prime p such that p mod primepi(p) = n.

Original entry on oeis.org

2, 3, 5, 7, 379, 23, 401, 61, 59, 29, 67, 71, 467, 79, 83, 179, 431, 89, 176557, 191, 24419, 491, 97, 101, 499, 1213, 3169, 3191, 523, 229, 3187, 223, 3203, 8609, 3163, 251, 176509, 257, 24509, 263, 3253, 269, 547, 3347, 1304867, 293

Offset: 0

Robert G. Wilson v, Feb 20 2023

nonn

Inspired by A048891.

			For n=0, prime p=2 has p mod primepi(p) = 2 mod 1 = 0 so that a(0) = 2.
For n=4, no prime has p mod primepi(p) = 4 until reaching p=379 which is 379 mod 75 = 4, so that a(4) = 379.

Robert G. Wilson v, Table of n, a(n) for n = 0..19217

Cf. A038625, A004648, A048891, A052013, A073325, A073436, A162567, A171430, A171431, A171432, A171434.

V:= Array(0..100): count:= 0:
p:= 1:
for k from 1 while count < 101 do
  p:= nextprime(p);
  v:= p mod k;
  if v <= 100 and V[v] = 0 then V[v]:= p; count:= count+1 fi;
od:
convert(V,list); # Robert Israel, Feb 28 2023

t[_] := 0; p = 2; pi = 1; While[p < 1400000, m = Mod[p, pi]; If[m < 100 && t[m] == 0, t[m] = p]; p = NextPrime@p; pi++]; t /@ Range[0, 99]

a(n)={my(k=n); forprime(p=prime(n+1), oo, k++; if(p%k ==n, return(p)))} \\ Andrew Howroyd, Feb 21 2023

from sympy import prime, nextprime
def A360789(n):
    p, m = prime(n+1), n+1
    while p%m != n:
        p = nextprime(p)
        m += 1
    return p # Chai Wah Wu, Mar 18 2023

a(n) = prime(A073325(n+1)). - Kevin Ryde, Feb 21 2023

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

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A078931 Numbers k that divide prime(k)+1 or prime(k)-1.

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A360789 Least prime p such that p mod primepi(p) = n.

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