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A224502 Prime numbers (together with one) whose representation in balanced ternary are palindromes.

%I A224502 #22 May 13 2013 01:54:23
%S A224502 1,7,13,43,61,73,103,367,421,457,547,601,613,757,859,1039,1093,3823,
%T A224502 4021,4561,4723,4759,5743,6211,6373,6481,6949,7219,7489,7933,8563,
%U A224502 8941,9103,9679,29527,30013,31147,31741,33037,35251,36061,36097,36583,37717,39607,41011,42667,43963,44773,45691,47581,49201
%N A224502 Prime numbers (together with one) whose representation in balanced ternary are palindromes.
%C A224502 Intersection of A006005 and A134027.
%H A224502 Malachi de Ælfweald and Charles R Greathouse IV, <a href="/A224502/b224502.txt">Table of n, a(n) for n = 1..10000</a> (first 199 terms from Malachi de Ælfweald)
%H A224502 Wikipedia, <a href="http://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>
%e A224502 For n=5, a(5)=61 and in balanced ternary notation is 1ī1ī1.
%o A224502 (PARI)
%o A224502 bt(k,n)={
%o A224502     sum(i=0,(n-1)\2,
%o A224502         my(t=k%3-1);
%o A224502         k\=3;
%o A224502         n--;
%o A224502         if(n==i,3^n,3^i+3^n)*t
%o A224502     )
%o A224502 };
%o A224502 do(N)={
%o A224502     my(v=List([1]),t);
%o A224502     for(n=1,N,
%o A224502         forstep(k=2,3^((n+1)\2)-1,3,
%o A224502             t=bt(k,n);
%o A224502             if(isprime(t),listput(v,t))
%o A224502         )
%o A224502     );
%o A224502     vecsort(Vec(v))
%o A224502 }; \\ _Charles R Greathouse IV_, Apr 08 2013
%K A224502 nonn,base
%O A224502 1,2
%A A224502 _Malachi de Ælfweald_, Apr 08 2013