A279756 - OEIS

%I #25 Jan 04 2024 16:22:57

%S 2,5,7,23,13,41,19,59,71,31,157,113,43,131,331,373,61,307,337,73,367,

%T 239,251,269,293,103,311,109,547,1019,383,919,139,419,151,757,787,491,

%U 503,521,181,907,193,967,199,599,1901,1117,229,2063,701,241,3617,1759,773

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

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

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

%H Alois P. Heinz, <a href="/A279756/b279756.txt">Table of n, a(n) for n = 1..10000</a>

%p a:= proc(n) local q, p; p:= ithprime(n); q:= p;

%p       do if irem(q-2, p)=0 then break fi;

%p          q:= nextprime(q);

%p       od; q

%p     end:

%p seq(a(n), n=1..55);  # _Alois P. Heinz_, May 03 2021

%o (PARI) a(n) = {p = prime(n); q = p; while (Mod(q, p) != 2, q = nextprime(q+1)); q;} \\ _Michel Marcus_, Dec 18 2016

%o (Python)

%o from itertools import dropwhile, count

%o from sympy import isprime, prime

%o 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

%Y A006512 is a subsequence.

%Y Cf. A000040, A034694.

%K nonn

%O 1,1

%A _Thomas Ordowski_ and _Altug Alkan_, Dec 18 2016