A100722 Prime numbers whose binary representations are split into exactly five runs.

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

Offset

1,1

Comments

The n-th prime is a term iff A100714(n)=5.

Links

Table of n, a(n) for n=1..53.

Eric Weisstein's World of Mathematics, Run-Length Encoding.

Example

a(3)=43 is a term because it is the 3rd prime whose binary representation splits into exactly five runs. 43_10 = 101011_2 splits into {{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