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Search: id:A051006
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| A051006 |
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Prime constant: decimal value of (A010051 interpreted as a binary number). |
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+0
30
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| 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, 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, 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
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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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).
"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.
"Examples of the inverse mapping are A092855 and A092857."
Prime[k]. Prime Constant C = Sum[ 1/2^Prime[k], {k,1,Infinity}]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 22 2006
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,20000
Ferenc Adorjan, Binary mapping of monotonic sequences and the Aronson function
S. Plouffe, Primes coded in binary to 1000 digits
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, World of Mathematics: Characteristic Function
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EXAMPLE
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0.414682509851111660... (base 10) = .01101010001010001010001... (base 2).
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MATHEMATICA
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RealDigits[ FromDigits[ {{Table[ If[ PrimeQ[n], 1, 0], {n, 370}]}, 0}, 2], 10, 111][[1]] (from Robert G. Wilson v Jan 15 2005)
RealDigits[Sum[1/2^Prime[k], {k, 1, 1000}], 10, 100] - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 22 2006
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PROGRAM
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(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)
(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]
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CROSSREFS
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Cf. A010051, A051007.
Cf. A092855, A092857, A092858, A092859, A092860, A092861, A092862, A092863, A092874.
Sequence in context: A167431 A110361 A092856 this_sequence A072812 A162956 A131112
Adjacent sequences: A051003 A051004 A051005 this_sequence A051007 A051008 A051009
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KEYWORD
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nonn,cons
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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