

A051006


Prime constant: decimal value of (A010051 interpreted as a binary number).


33



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;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

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 nth fractional digit is 1 if and only if n is in the sequence.
"Examples of the inverse mapping are A092855 and A092857." (End)


LINKS

Harry J. Smith, Table of n, a(n) for n = 0..20000
Ferenc Adorjan, Binary mapping of monotonic sequences and the Aronson function
Simon Plouffe, Primes coded in binary to 1000 digits
Eric Weisstein's World of Mathematics, Prime Constant
Eric Weisstein's World of Mathematics, World of Mathematics: Characteristic Function


FORMULA

Prime constant C = sum(k = 1 .. infinity, 1/2^p(k)), where p(k) is the kth prime.  Alexander Adamchuk, Aug 22 2006


EXAMPLE

0.414682509851111660... (base 10) = .01101010001010001010001... (base 2).


MATHEMATICA

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, 1000}], 10, 100][[1]] (* Alexander Adamchuk, Aug 22 2006 *)


PROG

(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=(xd)*10; write("b051006.txt", n, " ", d)); } \\ From Harry J. Smith, Jun 15 2009


CROSSREFS

Cf. A010051, A051007, A092855, A092857, A092858, A092859, A092860, A092861, A092862, A092863, A092874.
Sequence in context: A193750 A092856 A072812 * A162956 A131112 A141225
Adjacent sequences: A051003 A051004 A051005 * A051007 A051008 A051009


KEYWORD

nonn,cons,changed


AUTHOR

Eric W. Weisstein


STATUS

approved



