A087510 Primes consisting only of digits 0 and 1 occurring with equal frequency.

10010101, 10100011, 1000011011, 1000110101, 1001000111, 1001001011, 1001010011, 1010000111, 1010001101, 1010010011, 1010100011, 1010110001, 1011000101, 1100001101, 1101001001, 10000101011101, 10000111100011, 10000111110001, 10001000011111, 10001001011011

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).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..18167 (first 1000 terms from T. D. Noe)

Crossrefs

Primes in A071925.

The 18 sequences in this family are: this sequence (1,0), A087511 (1,3), A087512 (1,4), A087513 (1,6), A087514 (1,7), A087515 (1,9), A087527 (2,3), A087528 (2,9), A087529 (3,4), A087530 (3,5), A087531 (3,7), A087532 (3,8), A087533 (4,7), A087534 (4,9), A087535 (5,9), A087536 (6,7), A087537 (7,9), A087538 (8,9).

Programs

Mathematica

Select[FromDigits/@Tuples[{0,1},14],PrimeQ[#] && Length[x=IntegerDigits[#]]==2*Count[x,0] &] (* Jayanta Basu, May 23 2013 *)

PARI

\\ B(k,d1,d2,pred) k-digits of (d1,d2) each, satisfying pred.
B(k,d1,d2,pred)={my(L=List(),m=10^(2*k-1)); forsubset([2*k,k], s, my(t=(10^(2*k)-1)/9*d1 + (d2-d1)*sum(i=1, #s, 10^(s[i]-1))); if(t>=m && pred(t), listput(L,t))); vecsort(Vec(L))}
{ concat(vector(7,k,B(k,0,1,isprime)))[1..20] } \\ Andrew Howroyd, Sep 20 2024