Search: id:A051006
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%I A051006
%S A051006 4,1,4,6,8,2,5,0,9,8,5,1,1,1,1,6,6,0,2,4,8,1,0,9,6,2,2,1,5,4,3,0,7,7,0,
%T A051006 8,3,6,5,7,7,4,2,3,8,1,3,7,9,1,6,9,7,7,8,6,8,2,4,5,4,1,4,4,8,8,6,4,0,9,
%U A051006 6,0,6,1,9,3,5,7,3,3,4,1,9,6,2,9,0,0,4,8,4,2,8,4,7,5,7,7,7,9,3,9,6,1,6
%N A051006 Prime constant: decimal value of (A010051 interpreted as a binary number).
%C A051006 Comments from Ferenc Adorjan (fadorjan(AT)freemail.hu): "Decimal expansion 
               of the representation of the sequence of primes by a single real 
               in (0,1).
%C A051006 "Any monotonic integer sequence can be represented by a real number in 
               (0,1) such a way that in the binary representation of the real, the 
               n-th fractional digit is 1 iff n is in the sequence.
%C A051006 "Examples of the inverse mapping are A092855 and A092857."
%C A051006 Prime[k]. Prime Constant C = Sum[ 1/2^Prime[k], {k,1,Infinity}]. - Alexander 
               Adamchuk (alex(AT)kolmogorov.com), Aug 22 2006
%H A051006 Harry J. Smith, <a href="b051006.txt">Table of n, a(n) for n=0,...,20000</
               a>
%H A051006 Ferenc Adorjan, <a href="http://web.axelero.hu/fadorjan/aronsf.pdf">Binary 
               mapping of monotonic sequences and the Aronson function</a>
%H A051006 S. Plouffe, <a href="http://pi.lacim.uqam.ca/piDATA/primesbin.txt">Primes 
               coded in binary to 1000 digits</a>
%H A051006 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimeConstant.html">Link to a section of The World of Mathematics.</
               a>
%H A051006 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CharacteristicFunction.html">World of Mathematics: Characteristic 
               Function</a>
%e A051006 0.414682509851111660... (base 10) = .01101010001010001010001... (base 
               2).
%t A051006 RealDigits[ FromDigits[ {{Table[ If[ PrimeQ[n], 1, 0], {n, 370}]}, 0}, 
               2], 10, 111][[1]] (from Robert G. Wilson v Jan 15 2005)
%t A051006 RealDigits[Sum[1/2^Prime[k],{k,1,1000}],10,100] - Alexander Adamchuk 
               (alex(AT)kolmogorov.com), Aug 22 2006
%o A051006 (PARI) { mt(v)= /*Returns the binary mapping of v monotonic sequence 
               as a real in (0,1)*/ local(a=0.0,p=1,l);l=matsize(v)[2]; for(i=1,
               l,a+=2^(-v[i])); return(a)} (Ferenc Adorjan)
%o A051006 (PARI) { default(realprecision, 20080); x=0; m=67000; for (n=1, m, if 
               (isprime(n), a=1, a=0); x=2*x+a; ); x=10*x/2^m; for (n=0, 20000, 
               d=floor(x); x=(x-d)*10; write("b051006.txt", n, " ", d)); } [From 
               Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 15 2009]
%Y A051006 Cf. A010051, A051007.
%Y A051006 Cf. A092855, A092857, A092858, A092859, A092860, A092861, A092862, A092863, 
               A092874.
%Y A051006 Sequence in context: A167431 A110361 A092856 this_sequence A072812 A162956 
               A131112
%Y A051006 Adjacent sequences: A051003 A051004 A051005 this_sequence A051007 A051008 
               A051009
%K A051006 nonn,cons
%O A051006 0,1
%A A051006 Eric Weisstein (eric(AT)weisstein.com)

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