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A341284 a(n) is the least prime == -prime(n) (mod 2*prime(n+1)).

%I A341284 #37 Feb 26 2021 13:40:54
%S A341284 7,23,37,41,89,59,73,151,157,43,127,131,239,59,419,307,73,359,367,401,
%T A341284 419,1163,881,307,311,967,547,569,3697,397,691,419,457,757,163,821,
%U A341284 839,179,1259,907,2111,967,1777,599,223,3803,3863,2063,3499,1201,3617,2269,263,269,1889,2441,283,1409
%N A341284 a(n) is the least prime == -prime(n) (mod 2*prime(n+1)).
%C A341284 a(k) is the least odd prime == -prime(k) (mod prime(k+1)).
%C A341284 a(k) = A163981(k) if and only if k is not in A029707.
%C A341284 a(k) = 2*prime(k+1)-prime(k) if and only if prime(k+1) is in A071680.
%H A341284 Robert Israel, <a href="/A341284/b341284.txt">Table of n, a(n) for n = 2..10000</a>
%F A341284 (a(k) + prime(k)) mod (2*prime(k+1)) = 0.
%e A341284 a(3) = 23 is the least prime == -5 (mod 14), where prime(3) = 5 and prime(4) = 7.
%p A341284 f:= proc(n) local k;
%p A341284   for k from 2*ithprime(n+1)-ithprime(n) by 2*ithprime(n+1)  do
%p A341284     if isprime(k) then return k fi
%p A341284   od;
%p A341284 end proc:
%p A341284 map(f, [$2..100]);
%o A341284 (PARI) a(n) = forprime(p=2,, if (Mod(p, 2*prime(n+1)) == -prime(n), return (p))); \\ _Michel Marcus_, Feb 25 2021
%Y A341284 Cf. A029707, A071680, A163981, A342027.
%K A341284 nonn,look
%O A341284 2,1
%A A341284 _J. M. Bergot_ and _Robert Israel_, Feb 25 2021