A087530 Primes consisting only of digits 3 and 5 occurring with equal frequency.

53, 35553533, 53355353, 53533553, 3335553553, 3355335553, 3355355533, 3355533553, 3355535353, 3535355353, 3553535353, 3553555333, 3555353353, 3555353533, 3555533533, 5353353553, 5353533553, 5353553533, 5355353533

Offset

1,1

Comments

There are 18 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).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..5000

Mathematica

Sort[Select[FromDigits/@Flatten[Permutations/@Table[PadRight[{}, 2n, {3, 5}], {n, 5}], 1], PrimeQ]] (* Harvey P. Dale, Oct 24 2012 *)

Prog

(PARI) /* Primes consisting only of digits x and y, occurring with equal frequency. */ x=3; y=5; d1=x; d2=y; 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, A087511, A087529.

Sequence in context: A336440 A368298 A145332 * A125037 A101365 A022080

Adjacent sequences: A087527 A087528 A087529 * A087531 A087532 A087533

Keyword

base,nonn

Author

Amarnath Murthy and Paul D. Hanna, Sep 12 2003

Extensions

Edited by Charles R Greathouse IV, Oct 28 2009

Status

approved