A126555 - OEIS

%I #12 Sep 19 2024 04:18:06

%S 29,1439,4211,7703,12907,14957,16703,20947,29221,31189,33053,36749,

%T 44531,51437,90247,115547,124783,127163,133337,144511,146449,151339,

%U 157133,166219,169241,180233,181031,185123,197383,223367,225287,240347

%N Primes in A126554.

%C Primes that are the arithmetic mean of two consecutive balanced primes (of order one); primes of the form (A006562(k)+A006562(k+1))/2.

%C Might be called prime interprimes of order two.

%H Amiram Eldar, <a href="/A126555/b126555.txt">Table of n, a(n) for n = 1..10000</a>

%t b = {}; a = {}; Do[If[PrimeQ[((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2], AppendTo[a, ((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2]], {n, 1,10000}];Do[If[PrimeQ[(a[[k + 1]] + a[[k]])/2], AppendTo[b, (a[[k + 1]] + a[[k]])/2]], {k, 1, Length[a] - 1}]; b

%o (PARI) {m=250000;a=0;p=2;q=3;r=5;while(r<=m,if((p+r)/2==q,if(a>0,if(isprime(b=(a+q)/2),print1(b,",")));a=q);p=q;q=r;r=nextprime(r+1))} \\ _Klaus Brockhaus_, Jan 05 2007

%Y Cf. A126554, A006562.

%K nonn

%O 1,1

%A _Artur Jasinski_, Dec 27 2006

%E Edited and extended by _Klaus Brockhaus_, Jan 05 2007