A087952 Smallest prime == 1 (mod n) and > n^2.

2, 5, 13, 17, 31, 37, 71, 73, 109, 101, 199, 157, 313, 197, 241, 257, 307, 379, 419, 401, 463, 617, 599, 577, 701, 677, 757, 953, 929, 991, 1117, 1153, 1123, 1259, 1471, 1297, 1481, 1483, 1873, 1601, 1723, 1933, 1979, 2069, 2161, 2347, 2351, 2593, 2549, 2551

Offset: 1

Author

Ray Chandler, Sep 16 2003

Keywords

• nonn

Comments

Primes arising in A087554.

Since A014085(n) ~ n/log(n) one may conjecture that a(n) < 2*n^2 for all n > 1. Numerically we find a(n) = n^2*(1 + O(1/sqrt(n))). - M. F. Hasler, Feb 27 2020

Examples

			For n=1, a(1) = 2, because 2 == 1 mod 1 and 2 > 1^2.
For n=2, a(2) = 5, because 5 == 1 mod 2 and 5 > 2^2.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..10000, Feb 27 2020

Crossrefs

Cf. A034693, A034694, A087554.

Cf. A014085 (number of primes between n^2 and (n+1)^2).

Programs

Mathematica

spr[n_]:=Module[{p=NextPrime[n^2]},While[Mod[p,n]!=1,p=NextPrime[p]];p]; Join[ {2},Array[spr,50,2]] (* Harvey P. Dale, Jun 21 2021 *)

PARI

apply( {A087952(n)=forprime(p=n^2+1,,(p-1)%n||return(p))}, [1..66]) \\ M. F. Hasler, Feb 27 2020

Extensions

Examples added by N. J. A. Sloane, Jun 21 2021