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A087511
Primes consisting only of digits 1 and 3 occurring with equal frequency.
20
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
1,1
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
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) \\ Needs B() from A087510.
concat(vector(6, k, B(k, 1, 3, isprime))) \\ Andrew Howroyd, Sep 21 2024
CROSSREFS
KEYWORD
base,nonn
AUTHOR
STATUS
approved