A087511 Primes consisting only of digits 1 and 3 occurring with equal frequency.

13, 31, 11313331, 11333131, 13111333, 13131133, 13131331, 13133311, 13311313, 31133131, 33113131, 1113131333, 1131131333, 1131311333, 1131331133, 1133111333, 1133113133, 1133133311, 1133311313, 1133313113, 1133313131

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