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A119523 Decimal expansion of 2^-1 + 2^-2 + 2^-4 + 2^-6 + 2^-10 + ..., where the exponents are 1 less than the primes. 3
8, 2, 9, 3, 6, 5, 0, 1, 9, 7, 0, 2, 2, 2, 3, 3, 2, 0, 4, 9, 6, 2, 1, 9, 2, 4, 4, 3, 0, 8, 6, 1, 5, 4, 1, 6, 7, 3, 1, 5, 4, 8, 4, 7, 6, 2, 7, 5, 8, 3, 3, 9, 5, 5, 7, 3, 6, 4, 9, 0, 8, 2, 8, 9, 7, 7, 2, 8, 1, 9, 2, 1, 2, 3, 8, 7, 1, 4, 6, 6, 8, 3, 9, 2, 5, 8, 0, 0, 9, 6, 8, 5, 6, 9, 5, 1, 5, 5, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Decimal expansion of Sum_{ k >= 1} A010051(k)/2^(k-1).

The primes have a larger measure than the composites as they dominate the lower integers.

The binary JIS function (as defined in A113829) for this constant (that we may call the van der Waerden-Ulam constant W) is given by the first differences of A000720, A000720(n+1)-A000720(n)= A010051(n+1)= JIS[W,2]. - Artur Jasinski, Jun 02 2008

REFERENCES

S. M. Ulam, Problems in Modern Mathematics, John Wiley and Sons, New York, 1960, page 54

LINKS

Table of n, a(n) for n=0..99.

FORMULA

Equals 2*A051006 = 1/2 + 1/4 + 1/16 + 1/64 + 1/1024 +1/4096 + 1/65536 + .. (see A061286)

EXAMPLE

0.829365...

MATHEMATICA

b = 0; Do[k = PrimePi[n + 1] - PrimePi[n]; b = b + k/2^n, {n, 1, 200}]; First[RealDigits[N[b, 200]]] (* Artur Jasinski, Jun 02 2008 *)

PROG

(PARI) s=0; forprime(p=2, 1000, s+=1.>>p); 2*s \\ Charles R Greathouse IV, Apr 05 2012

CROSSREFS

Cf. A000720, A119524 (measure of composites), A010051, A113829.

Sequence in context: A278261 A019865 A198993 * A181164 A154212 A155035

Adjacent sequences:  A119520 A119521 A119522 * A119524 A119525 A119526

KEYWORD

nonn,cons

AUTHOR

Roger L. Bagula, May 27 2006

EXTENSIONS

More terms from Peter Pein (petsie(AT)dordos.net), May 31 2006

Edited by N. J. A. Sloane, Nov 17 2006

Corrected use of PrimePi in the first comment line - R. J. Mathar, Oct 30 2010, Alonso Del Arte, Apr 05 2012

STATUS

approved

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Last modified March 29 15:10 EDT 2017. Contains 284273 sequences.