A279756 Smallest prime p >= prime(n) such that p == 2 (mod prime(n)).

2, 5, 7, 23, 13, 41, 19, 59, 71, 31, 157, 113, 43, 131, 331, 373, 61, 307, 337, 73, 367, 239, 251, 269, 293, 103, 311, 109, 547, 1019, 383, 919, 139, 419, 151, 757, 787, 491, 503, 521, 181, 907, 193, 967, 199, 599, 1901, 1117, 229, 2063, 701, 241, 3617, 1759, 773

Offset: 1

Author

Thomas Ordowski and Altug Alkan, Dec 18 2016

Keywords

• nonn

Comments

Conjecture: a(n) < prime(n)^2 for every n.

If this conjecture is true, then no terms are repeated.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

A006512 is a subsequence.

Cf. A000040, A034694.

Programs

Maple

a:= proc(n) local q, p; p:= ithprime(n); q:= p;
      do if irem(q-2, p)=0 then break fi;
         q:= nextprime(q);
      od; q
    end:
seq(a(n), n=1..55);  # Alois P. Heinz, May 03 2021

Mathematica

a[n_] := Module[{p = Prime[n], q}, q = p; While[True, If[Mod[q-2, p] == 0, Break[], q = NextPrime[q]]]; q];
Table[a[n], {n, 1, 55}] (* Jean-François Alcover, Jun 13 2025, after Alois P. Heinz *)

PARI

a(n) = {p = prime(n); q = p; while (Mod(q, p) != 2, q = nextprime(q+1)); q;} \\ Michel Marcus, Dec 18 2016

Python

from itertools import dropwhile, count
from sympy import isprime, prime
def A279756(n): return next(dropwhile(lambda x:not isprime(x),count(2 if (p:=prime(n))==2 else p+2,p))) # Chai Wah Wu, Jan 04 2024