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A092938 a(n) = least prime p such that 2*prime(n) - p is prime.

%I A092938 #14 Feb 07 2023 08:34:16
%S A092938 2,3,3,3,3,3,3,7,3,5,3,3,3,3,5,3,5,13,3,3,7,7,3,5,3,3,7,3,7,3,3,5,3,7,
%T A092938 5,19,3,13,3,29,5,3,3,3,5,19,3,3,5,19,3,11,3,3,5,3,17,19,7,5,3,17,7,3,
%U A092938 7,3,3,13,3,7,5,17,7,3,7,5,5,7,5,7,11,3,3,3,19,3,11,3,3,7,5,5,3,5,7,23,5,3
%N A092938 a(n) = least prime p such that 2*prime(n) - p is prime.
%C A092938 a(n) = least prime p such that prime(n) = (p+q)/2, where q is also prime.
%C A092938 a(n) <= prime(n). Conjecture: a(n) = prime(n) only for n = 1 and 2.
%H A092938 Robert Israel, <a href="/A092938/b092938.txt">Table of n, a(n) for n = 1..10000</a>
%e A092938 2*prime(8) = 38; 38 - 2 = 36, 38 - 3 = 35, 38 - 5 = 33 are composite, but 38 - 7 = 31 is prime. Hence a(8) = 7.
%p A092938 f:= proc(n) local pn,p;
%p A092938    pn:= ithprime(n);
%p A092938    p:= 1;
%p A092938    do
%p A092938      p:= nextprime(p);
%p A092938      if isprime(2*pn-p) then return p fi
%p A092938    od
%p A092938 end proc:
%p A092938 map(f, [$1..100]); # _Robert Israel_, Jul 31 2020
%t A092938 a[n_] := Module[{p, q = Prime[n]}, For[p = 2, True, p = NextPrime[p], If[PrimeQ[2q-p], Return[p]]]];
%t A092938 Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Feb 07 2023 *)
%o A092938 (PARI) {for(n=1, 98, k=2*prime(n); p=2; while(!isprime(k-p), p=nextprime(p+1)); print1(p,","))} \\ _Klaus Brockhaus_, Dec 23 2006
%Y A092938 Cf. A092939, A092940, A116619.
%K A092938 nonn
%O A092938 1,1
%A A092938 _Amarnath Murthy_, Mar 23 2004
%E A092938 Edited and extended by _Klaus Brockhaus_, Dec 23 2006