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%I #8 Aug 08 2017 11:57:47
%S 43,34434343,44334343,44343433,3334344443,3343443443,3344334443,
%T 3344344343,3344434433,3433434443,3433444433,3434444333,3443343443,
%U 3444334343,4334433443,4334443433,4343444333,4344333443,4344433343
%N Primes consisting only of digits 4 and 3 occurring with equal frequency.
%C There are 18 digit pairs which can produce such primes. (1,0),(7,0),(1,3),(1,4),(1,6),(1,7),(1,9),(2,3),(2,9),(3,4),(3,5),(3,7),(3,8),(4,7),(4,9),(5,9),(6,7),(7,9).
%H Harvey P. Dale, <a href="/A087529/b087529.txt">Table of n, a(n) for n = 1..5000</a>
%p Primes consisting only of digits x and y, occurring with equal frequency. d1=x; d2=y; k=0; a=vector(100); for(n=1,3000,B=binary(n); L=length(B); s=sum(j=1,length(B),B[j]); if(L%2==0 & s==L/2, C=vector(L,n,(d2-d1)*B[n]+d1); p=subst(Pol(C),x,10); if(isprime(p),if(k<100,k++; a[k]=p)); D=vector(L,n,d2-(d2-d1)*B[n]); q=subst(Pol(D),x,10); if(isprime(q ),if(k<100,k++; a[k]=q))); ); a=vector(k,n,a[n]); vecsort(a)
%t Select[FromDigits/@Flatten[Permutations/@Table[PadRight[{},2n,{4,3}],{n,5}],1],PrimeQ]//Sort (* _Harvey P. Dale_, Aug 08 2017 *)
%Y Cf. A087510, A087511, A087528.
%K base,nonn
%O 1,1
%A _Paul D. Hanna_ and _Amarnath Murthy_, Sep 12 2003
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