A087533 Primes consisting only of digits 4 and 7 occurring with equal frequency.

47, 47447747, 77474447, 4447747747, 4744477747, 4744747477, 4744747747, 4747444777, 4747747447, 4774744477, 4774747447, 7444477477, 7447474477, 7744744747, 7744747447, 7747444477, 7747447447, 7747744447, 44444477777477, 44447447774777, 44447474777477

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..10000

Mathematica

Table[Select[FromDigits/@Permutations[PadRight[{}, 2n, {4, 7}]], PrimeQ], {n, 7}]//Flatten//Sort (* Harvey P. Dale, May 05 2016 *)

Prog

(PARI) /* Primes consisting only of digits x and y, occurring with equal frequency. */ x=4; 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, A087532.

Sequence in context: A224468 A353697 A328364 * A292071 A292707 A292967

Adjacent sequences: A087530 A087531 A087532 * A087534 A087535 A087536

Keyword

base,nonn

Author

Paul D. Hanna and Amarnath Murthy, Sep 12 2003

Extensions

Edited by Charles R Greathouse IV, Oct 28 2009

Corrected by Harvey P. Dale, May 05 2016

Status

approved