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A087510
Primes consisting only of digits 0 and 1 occurring with equal frequency.
20
10010101, 10100011, 1000011011, 1000110101, 1001000111, 1001001011, 1001010011, 1010000111, 1010001101, 1010010011, 1010100011, 1010110001, 1011000101, 1100001101, 1101001001, 10000101011101, 10000111100011, 10000111110001, 10001000011111, 10001001011011
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).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..18167 (first 1000 terms from T. D. Noe)
MATHEMATICA
Select[FromDigits/@Tuples[{0, 1}, 14], PrimeQ[#] && Length[x=IntegerDigits[#]]==2*Count[x, 0] &] (* Jayanta Basu, May 23 2013 *)
PROG
(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
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).
Sequence in context: A182749 A260915 A072144 * A173002 A139120 A210893
KEYWORD
base,nonn
AUTHOR
STATUS
approved