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%I #4 Dec 05 2013 19:56:46
%S 2,3,7,11,19,23,31,31,43,53,59,71,79,83,89,103,113,109,131,139,139,
%T 151,163,173,191,199,199,211,211,223,251,257,271,271,293,283,311,313,
%U 331,317,353,359,379,383,389,379,419,443,449,439,463,467,479,499,509,523
%N a(n) = largest prime p such that 2*prime(n) - p is prime.
%C a(n) = largest prime p such that prime(n) = (p+q)/2, where q is also prime.
%C prime(n) <= a(n) < 2*prime(n).
%C Conjecture: a(n) = prime(n) only for n = 1 and 2.
%F a(n) = 2*prime(n) - A092938(n).
%e 2*prime(18) = 122; the primes smaller than 122 are 113, 109, 107, ... in descending order. 122 - 113 = 9 is not prime, but 122 - 109 = 13 is prime, hence a(18) = 109.
%o (PARI) {for(n=1,56,k=2*prime(n);q=2;while(!isprime(p=k-q),q=nextprime(q+1));print1(p,","))} - Klaus Brockhaus, Dec 23 2006
%Y Cf. A092938, A092939, 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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