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Search: id:A100722
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| A100722 |
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Prime numbers whose binary representations are split into exactly five runs. |
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+0
1
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| 37, 41, 43, 53, 73, 83, 89, 101, 107, 109, 137, 139, 151, 157, 163, 167, 179, 197, 211, 229, 233, 269, 281, 283, 307, 311, 313, 317, 353, 359, 367, 379, 389, 397, 401, 409, 419, 431, 433, 439, 443, 457, 461, 467, 491, 521, 523, 541, 547, 563, 569, 571, 577
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The n-th prime is a member iff A100714(n)=5
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LINKS
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Eric Weisstein's World of Mathematics, "Run-Length Encoding."
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EXAMPLE
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a(3)=43 is a member because it is the 3rd prime whose binary representation splits into exactly five runs. 43_10=101011_2 splits to {{1}, {0}, {1}, {0}, {1,1}}
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MATHEMATICA
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Select[Table[Prime[k], {k, 1, 50000}], Length[Split[IntegerDigits[ #, 2]]] == 5 &]
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CROSSREFS
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Cf. A100714, A000040.
Sequence in context: A071855 A137675 A161725 this_sequence A093690 A090263 A033225
Adjacent sequences: A100719 A100720 A100721 this_sequence A100723 A100724 A100725
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KEYWORD
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base,nonn
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AUTHOR
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Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 11 2004
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