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A051006 Prime constant: decimal value of (A010051 interpreted as a binary number). 34
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 n-th 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} 1/2^p(k), where p(k) is the k-th 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]] (* 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=(x-d)*10; write("b051006.txt", n, " ", d)); } \\ 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 * A244097 A162956 A131112

Adjacent sequences:  A051003 A051004 A051005 * A051007 A051008 A051009

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified February 6 20:58 EST 2016. Contains 268049 sequences.