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A175452 a(n) = smallest prime such that a(n)+2 is multiple of 2n+1.

%I A175452 #7 Jul 03 2021 10:57:36
%S A175452 7,3,5,7,31,11,13,83,17,19,67,23,79,317,29,31,103,109,37,367,41,43,
%T A175452 139,47,151,157,53,283,293,59,61,193,199,67,211,71,73,229,709,79,911,
%U A175452 83,433,443,89,277,283,677,97,503,101,103,2459,107,109,337,113,349,593,1087
%N A175452 a(n) = smallest prime such that a(n)+2 is multiple of 2n+1.
%C A175452 Terms appearing twice:  a(1)=a(4)=7, a(5)=a(16)=31,...,
%C A175452 terms appearing thrice: a(28)=a(47)=a(142)=283, a(20)=a(61)=a(184)=367, etc.
%H A175452 Michael S. Branicky, <a href="/A175452/b175452.txt">Table of n, a(n) for n = 1..10000</a>
%e A175452 n=1: 7+2 is multiple of 3, n=2: 3+2 is multiple of 5, n=5: 31+2 is multiple of 11, n=8: 83+2 is multiple of 17.
%t A175452 s={};Do[k=2;While[Mod[2+(p=Prime[k]),n]>0,k++ ];AppendTo[s,p],{n,3,2001,2}];s
%o A175452 (Python)
%o A175452 from sympy import nextprime
%o A175452 def a(n):
%o A175452     p, m = 2, 2*n+1
%o A175452     while (p+2)%m: p = nextprime(p)
%o A175452     return p
%o A175452 print([a(n) for n in range(1, 61)]) # _Michael S. Branicky_, Jul 03 2021
%o A175452 (PARI) a(n) = my(p=2); while ((p+2) % (2*n+1), p = nextprime(p+1)); p; \\ _Michel Marcus_, Jul 03 2021
%Y A175452 Cf. A124199.
%K A175452 nonn
%O A175452 1,1
%A A175452 _Zak Seidov_, May 16 2010