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A348292
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Binary expansion of the smallest binary number starting with a(0)=1 that is prime when the final number is 1 and composite when the final number is 0.
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0
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1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0
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COMMENTS
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The prime values generated by this sequence are also generated by A084435 (except for 2, which is only listed in A084435).
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REFERENCES
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Donald E. Knuth, The Art of Computer Programming, Vol. 2, Seminumerical Algorithms, problem 39, page 76.
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LINKS
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EXAMPLE
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For example, the binary numbers 1, 11, and 111 expressed in base 10 are 1, 3, and 7, which are prime with the exception of the first term. The next term in the binary number must be 0 because the binary number 1111 is composite.
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MATHEMATICA
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seq[len_] := Module[{s = {1}, k = 1, m = 1, d}, While[k < len, m *= 2; d = Boole@PrimeQ[m + 1]; m += d; AppendTo[s, d]; k++]; s]; seq[100] (* Amiram Eldar, Oct 19 2021 *)
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PROG
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(HTML/JavaScript)
<html>
<script>
binary="1";
for(k=0; k<30; k++)
{
if(isprime(parseInt(binary+"1", 2))==true)
{
binary=binary+"1";
}
if(isprime(parseInt(binary+"1", 2))==false)
{
binary=binary+"0";
}
}
document.write(binary);
function isprime(x)
{
for(i=2; i<(x-1); i++)
{
if(x%i==0)
{
return false;
}
}
return true;
}
</script>
</html>
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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