A100723 Prime numbers whose binary representations are split into exactly seven runs.

149, 173, 181, 277, 293, 331, 337, 347, 349, 373, 421, 557, 587, 593, 599, 601, 613, 617, 619, 653, 659, 673, 691, 701, 709, 727, 733, 757, 809, 811, 821, 857, 859, 877, 937, 941, 1061, 1069, 1093, 1097, 1117, 1129, 1163, 1171, 1181, 1187, 1201, 1213

Offset: 1

Author

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

Keywords

• base
• nonn

Comments

The n-th prime is a member iff A100714(n)=7

Examples

			a(3) = 181 is a member because it is the 3rd prime whose binary representation splits into exactly 7 runs: 181_10 = 10110101_2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Run-Length Encoding.

Crossrefs

Cf. A100714, A000040.

Programs

Maple

qprime:= proc(n) if isprime(n) then n fi end proc:
[seq(seq(seq(seq(seq(seq(seq(qprime(2^i1 - 2^i2 + 2^i3 - 2^i4 + 2^i5
- 2^i6 + 2^i7-1), i7 = 1..i6-1),i6=i5-1..2,-1),i5=3..i4-1),  i4=i3-1..4,-1),i3=5..i2-1),i2=i1-1..6,-1),i1=7..12)]; # Robert Israel, Nov 24 2020

Mathematica

Select[Table[Prime[k], {k, 1, 50000}], Length[Split[IntegerDigits[ #, 2]]] == 7 &]