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

%I A100723 #16 Feb 16 2025 08:32:55
%S A100723 149,173,181,277,293,331,337,347,349,373,421,557,587,593,599,601,613,
%T A100723 617,619,653,659,673,691,701,709,727,733,757,809,811,821,857,859,877,
%U A100723 937,941,1061,1069,1093,1097,1117,1129,1163,1171,1181,1187,1201,1213
%N A100723 Prime numbers whose binary representations are split into exactly seven runs.
%C A100723 The n-th prime is a member iff A100714(n)=7
%H A100723 Robert Israel, <a href="/A100723/b100723.txt">Table of n, a(n) for n = 1..10000</a>
%H A100723 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Run-LengthEncoding.html">Run-Length Encoding</a>.
%e A100723 a(3) = 181 is a member because it is the 3rd prime whose binary representation splits into exactly 7 runs: 181_10 = 10110101_2.
%p A100723 qprime:= proc(n) if isprime(n) then n fi end proc:
%p A100723 [seq(seq(seq(seq(seq(seq(seq(qprime(2^i1 - 2^i2 + 2^i3 - 2^i4 + 2^i5
%p A100723 - 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
%t A100723 Select[Table[Prime[k], {k, 1, 50000}], Length[Split[IntegerDigits[ #, 2]]] == 7 &]
%Y A100723 Cf. A100714, A000040.
%K A100723 base,nonn
%O A100723 1,1
%A A100723 Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 11 2004