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

1,1

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

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

Prog

(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

Crossrefs

A006512 is a subsequence.

Cf. A000040, A034694.

Sequence in context: A072953 A243394 A175552 * A103060 A256247 A243595

Adjacent sequences: A279753 A279754 A279755 * A279757 A279758 A279759

Keyword

nonn

Author

Thomas Ordowski and Altug Alkan, Dec 18 2016

Status

approved