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, 1133331113, 1311113333, 1311311333, 1311313313

Offset: 1

Author

Paul D. Hanna and Amarnath Murthy, Sep 11 2003

Keywords

• base
• nonn

Comments

There are 18 digit pairs which can produce such primes. (1, 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

Crossrefs

Cf. A087510, A087512, A087513.

Programs

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 *)

PARI

\\ Needs B() from A087510.
concat(vector(6,k,B(k,1,3,isprime))) \\ Andrew Howroyd, Sep 21 2024