A100723 - OEIS

%I #15 Nov 25 2020 07:05:59

%S 149,173,181,277,293,331,337,347,349,373,421,557,587,593,599,601,613,

%T 617,619,653,659,673,691,701,709,727,733,757,809,811,821,857,859,877,

%U 937,941,1061,1069,1093,1097,1117,1129,1163,1171,1181,1187,1201,1213

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

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

%H Robert Israel, <a href="/A100723/b100723.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Run-LengthEncoding.html">Run-Length Encoding</a>.

%e 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 qprime:= proc(n) if isprime(n) then n fi end proc:

%p [seq(seq(seq(seq(seq(seq(seq(qprime(2^i1 - 2^i2 + 2^i3 - 2^i4 + 2^i5

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

%Y Cf. A100714, A000040.

%K base,nonn

%O 1,1

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