A038700 Smallest prime == -1 (mod n).

2, 3, 2, 3, 19, 5, 13, 7, 17, 19, 43, 11, 103, 13, 29, 31, 67, 17, 37, 19, 41, 43, 137, 23, 149, 103, 53, 83, 173, 29, 61, 31, 131, 67, 139, 71, 73, 37, 233, 79, 163, 41, 257, 43, 89, 137, 281, 47, 97, 149, 101, 103, 211, 53, 109, 167, 113, 173, 353, 59, 487, 61, 251

Offset

1,1

Links

Vladimir Pletser, Table of n, a(n) for n = 1..20000 (first 1000 terms from Joerg Arndt)

Mathematica

f[n_] := Block[{k = n - 1}, While[ !PrimeQ@k, k += n]; k]; Array[f, 63] (* Robert G. Wilson v, Jun 09 2009 *)
With[{prs=Prime[Range[100]]}, Table[SelectFirst[prs, Mod[#, n]==n-1&], {n, 70}]] (* Harvey P. Dale, Apr 26 2023 *)

Prog

(PARI)
N=10^8;  default(primelimit, N);
a(n)=forprime(p=2, 10^7, if(p%n==n-1, return(p)));
/* Joerg Arndt, Apr 16 2013 */
(PARI) a(n)=my(j); while(!isprime(j++*n-1), ); j*n-1 \\ Charles R Greathouse IV, Apr 18 2013
(Python)
from sympy import nextprime
def A038700(n):
    m = 2
    while (q:=(m+1)%n):
        m = nextprime(m+n-1-q)
    return m # Chai Wah Wu, Mar 29 2026

Crossrefs

Cf. A034694.

Sequence in context: A138781 A224416 A282049 * A177799 A125767 A326991

Adjacent sequences: A038697 A038698 A038699 * A038701 A038702 A038703

Keyword

nonn,easy

Author

David W. Wilson

Status

approved