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%I #9 Mar 28 2020 04:28:44
%S 199532,329070,487630,664345,878455,974874,1030434,1183684,1329780,
%T 1453746,1550775,1568843,1573919,1618431,1693333,1829142,2087087,
%U 2262462,2348799,2438192,2811665,3436775,3900917,4270580,4830665
%N Arithmetic mean of two consecutive prime interprimes of third order: interprimes of fourth order.
%C For primes in this sequence (prime interprimes of fourth order) see A127364.
%H Amiram Eldar, <a href="/A126558/b126558.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = (A126557(n)+A126557(n+1))/2.
%o (PARI) {m=5000000;a=0;g=0;e=0;p=2;q=3;r=5;while(r<=m,if((p+r)/2==q,if(a>0,b=(a+q)/2;if(isprime(b),if(g>0,h=(g+b)/2;if(isprime(h),if(e>0,f=(e+h)/2;print1(f,","));e=h));g=b));a=q);p=q;q=r;r=nextprime(r+1))} \\ _Klaus Brockhaus_, Jan 11 2007
%Y Cf. A006562 (balanced primes), A024675 (interprimes), A126554 (interprimes of second order), A126555 (prime interprimes of second order), A126556 (interprimes of third order), A126557 (prime interprimes of third order).
%K nonn
%O 1,1
%A _Artur Jasinski_, Dec 27 2006
%E Edited and extended by _Klaus Brockhaus_, Jan 11 2007