A087531 Primes consisting only of digits 3 and 7 occurring with equal frequency.

37, 73, 33373777, 33773737, 37373773, 37377337, 73337377, 73337773, 73373737, 73773373, 77337373, 77733373, 3337737737, 3337777337, 3377733773, 3733377377, 3733733777, 3737733773, 3773333777, 3773337377, 3773733737, 3777333773

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

Table of n, a(n) for n=0..21.

Mathematica

Select[Flatten[Table[FromDigits/@Permutations[Join[Table[3, {i}], Table[7, {i}]]], {i, 7}]], PrimeQ] (from Harvey Dale)

Prog

(PARI) /* Primes consisting only of digits x and y, occurring with equal frequency. */ x=3; 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, A087530.

Sequence in context: A083990 A123815 A289732 * A283718 A085959 A145936

Adjacent sequences: A087528 A087529 A087530 * A087532 A087533 A087534

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