A087536 Primes consisting only of digits 6 and 7 occurring with equal frequency.

67, 67766767, 76767667, 6666767777, 6667677677, 6667776767, 6667777667, 6676766777, 6676767677, 6676776677, 6677666777, 6677667767, 6677676767, 6766677767, 6766776677, 6767667677, 6767677667, 6776766677, 6776766767

Offset

0,1

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 = 0..5000

Mathematica

Sort[Flatten[Table[Select[FromDigits/@Permutations[PadRight[{}, 2n, {6, 7}]], PrimeQ], {n, 5}]]] (* Harvey P. Dale, Dec 03 2012 *)

Prog

(PARI) /* Primes consisting only of digits x and y, occurring with equal frequency. */ x=6; y=7; 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, A087535.

Sequence in context: A367903 A279798 A191941 * A281888 A282338 A198210

Adjacent sequences: A087533 A087534 A087535 * A087537 A087538 A087539

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