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%I #14 Apr 09 2022 08:39:00
%S 53,173,263,373,563,593,653,733,1103,1123,1223,1753,2903,2963,3313,
%T 3733,4013,4993,5113,5303,5393,5563,6073,6263,6323,6373,6863,7523,
%U 7583,7823,8713,9473,10253,10853,11903,11933,12583,12653,12973,13043,13463,14543,14753
%N Balanced primes of order one ending in 3.
%H Harvey P. Dale, <a href="/A303093/b303093.txt">Table of n, a(n) for n = 1..1000</a>
%e 53 = (47 + 53 + 59)/3 = 159/3 and 53 = 5*10 + 3.
%p p:=ithprime: a:=n->`if`(add(p(n-k),k=-1..1)=3*p(n) and modp(p(n), 10) = 3,p(n),NULL): seq(a(n),n=3..2000);
%t Select[Partition[Prime[Range[2000]],3,1],Mean[#]==#[[2]]&&Mod[#[[2]],10]==3&][[All, 2]] (* _Harvey P. Dale_, Apr 09 2022 *)
%o (GAP) P:=Filtered([1..15000],IsPrime);;
%o a:=Filtered(List(Filtered(List([0..Length(P)-3],k->List([1..3],j->P[j+k])),i->Sum(i)/3=i[2]),m->m[2]),l-> l mod 10=3);
%Y Intersection of A006562 and A030431.
%Y Cf. A303092, A303094, A303095.
%K nonn,base
%O 1,1
%A _Muniru A Asiru_, Apr 18 2018
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