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 A087511 Primes consisting only of digits 1 and 3 occurring with equal frequency. 16
 13, 31, 11313331, 11333131, 13111333, 13131133, 13131331, 13133311, 13311313, 31133131, 33113131, 1113131333, 1131131333, 1131311333, 1131331133, 1133111333, 1133113133, 1133133311, 1133311313, 1133313113, 1133313131 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS There are 19 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), (8, 9). - corrected by Robert Israel, Jul 10 2018 The number of digits is even and not divisible by 3. - Robert Israel, Jul 09 2018 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 MAPLE sort(select(isprime, [seq(seq((10^(2*d)-1)/9+2*add(10^i, i=s), s=combinat:-choose([\$0..(2*d-1)], d)), d=[1, 2, 4, 5, 7, 8, 10])])); # Robert Israel, Jul 09 2018 MATHEMATICA Union[FromDigits/@Select[Flatten[Table[Tuples[{1, 3}, k], {k, 10}], 1], PrimeQ[FromDigits[#]] && Count[#, 1]==Count[#, 3] &]] (* Jayanta Basu, May 19 2013 *) PROG (PARI) d1=1; d2=3; 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) CROSSREFS Cf. A087510, A087512, A087513. Sequence in context: A247836 A159670 A238736 * A299449 A300087 A118513 Adjacent sequences: A087508 A087509 A087510 * A087512 A087513 A087514 KEYWORD base,nonn AUTHOR Paul D. Hanna and Amarnath Murthy, Sep 11 2003 STATUS approved

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Last modified April 22 07:09 EDT 2024. Contains 371888 sequences. (Running on oeis4.)