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Search: id:A087533
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| A087533 |
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Primes consisting only of digits 4 and 7 occurring with equal frequency. |
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+0
2
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| 47, 47447747, 77474447, 4447747747, 4744477747, 4744747477, 4744747747, 4747444777, 4747747447, 4774744477, 4774747447, 7444477477, 7447474477, 7744744747, 7744747447, 7747444477, 7747447447, 7747744447, 47744744477477
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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).
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PROGRAM
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(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)
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CROSSREFS
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Cf. A087510, A087511, A087532.
Sequence in context: A101629 A033520 A093940 this_sequence A023935 A002834 A057380
Adjacent sequences: A087530 A087531 A087532 this_sequence A087534 A087535 A087536
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KEYWORD
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base,nonn,new
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com) and Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 12 2003
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EXTENSIONS
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Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 28 2009
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