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A343691 a(n) is the least prime p such that p + A014574(n) is prime.

%I A343691 #9 Apr 27 2021 02:42:55
%S A343691 3,5,5,5,7,5,7,7,5,5,11,7,11,5,13,5,11,7,11,5,5,11,7,5,19,7,7,13,5,13,
%T A343691 11,5,11,5,5,11,7,11,7,5,11,7,5,7,5,7,5,7,5,5,5,7,29,11,11,13,5,11,17,
%U A343691 23,5,11,5,11,17,7,11,5,5,23,7,7,7,17,5,5,7,11,7,17,29,11,17,13,5,13,7,13
%N A343691 a(n) is the least prime p such that p + A014574(n) is prime.
%C A343691 a(n) >= 5 for n >= 2, since A014574(n) == 0 (mod 6).
%C A343691 a(n) = 5 if and only if A001359(n) is in A022004.
%H A343691 Robert Israel, <a href="/A343691/b343691.txt">Table of n, a(n) for n = 1..10000</a>
%e A343691 a(5) = 7 because A014574(5) = 30 and 7 is the least prime p such that 30+p is prime.
%p A343691 P:= {seq(ithprime(i),i=1..10^4)}:
%p A343691 A014574:= sort(convert(map(`+`,P,1) intersect map(`-`,P,1),list)):
%p A343691 f:= proc(n) local p,t;
%p A343691    p:= 2;
%p A343691    do
%p A343691       p:= nextprime(p);
%p A343691       if isprime(p+A014574[n]) then return p fi
%p A343691    od
%p A343691 end proc:
%p A343691 map(f, [$1..nops(A014574)]);
%Y A343691 Cf. A001359, A014574, A022004.
%K A343691 nonn
%O A343691 1,1
%A A343691 _J. M. Bergot_ and _Robert Israel_, Apr 26 2021