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A092938 a(n) = least prime p such that 2*prime(n) - p is prime. 3

%I

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

%C a(n) = least prime p such that prime(n) = (p+q)/2, where q is also prime.

%C a(n) <= prime(n). Conjecture: a(n) = prime(n) only for n = 1 and 2.

%H Robert Israel, <a href="/A092938/b092938.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 f:= proc(n) local pn,p;

%p pn:= ithprime(n);

%p p:= 1;

%p do

%p p:= nextprime(p);

%p if isprime(2*pn-p) then return p fi

%p od

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Jul 31 2020

%o (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 Cf. A092939, A092940, A116619.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Mar 23 2004

%E Edited and extended by _Klaus Brockhaus_, Dec 23 2006

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Last modified April 21 19:16 EDT 2021. Contains 343156 sequences. (Running on oeis4.)