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

Author

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

Keywords

• base
• nonn

Comments

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

Examples

			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}}.
		

Links

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

Crossrefs

Cf. A100714, A000668 (exactly 1 run), A082554 (exactly 3 runs), A100723 (exactly 7 runs).

Programs

Mathematica

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