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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. 5
 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 FORMULA Equals 2*A051006 = 1/2 + 1/4 + 1/16 + 1/64 + 1/1024 +1/4096 + 1/65536 + .. (see A061286) Equals Sum_{k>=1} pi(k)/2^k, where pi(k) = A000720(k). - Amiram Eldar, Aug 11 2020 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, A010051, A061286, A113829, A119524 (measure of composites). Sequence in context: A019865 A198993 A307565 * 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 January 19 12:46 EST 2021. Contains 340269 sequences. (Running on oeis4.)