

A100722


Prime numbers whose binary representations are split into exactly five runs.


0



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
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OFFSET

1,1


COMMENTS

The nth prime is a member iff A100714(n)=5


LINKS

Table of n, a(n) for n=1..53.
Eric Weisstein's World of Mathematics, "RunLength Encoding."


EXAMPLE

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}}


MATHEMATICA

Select[Table[Prime[k], {k, 1, 50000}], Length[Split[IntegerDigits[ #, 2]]] == 5 &]


CROSSREFS

Cf. A100714, A000040.
Sequence in context: A071855 A137675 A161725 * A093690 A288618 A090263
Adjacent sequences: A100719 A100720 A100721 * A100723 A100724 A100725


KEYWORD

base,nonn


AUTHOR

Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 11 2004


STATUS

approved



