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A119523
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Decimal expansion of the van der Waerden-Ulam binary measure of the primes.
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4
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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; internal format)
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OFFSET
| 0,1
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COMMENTS
| Decimal expansion of Sum_{ k >= 1} A010051(k)/2^k.
The primes have a larger measure than the composites as they dominate the lower integers.
Binary JIS function (definition see e.g. A113829) for van der Waerden-Ulam constant W (A119523)is given first differences of A000720 A000720(n+1)-A000720(n)=A010051(n+1)=JIS[W,2] where W=0.829365019702223320496219.. - Artur Jasinski (grafix(AT)csl.pl), Jun 02 2008
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REFERENCES
| S. M. Ulam, Problems in Modern Mathematics, John Wiley and Sons, New York, 1960, page 54
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EXAMPLE
| 0.829365...
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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 (grafix(AT)csl.pl), Jun 02 2008
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CROSSREFS
| Cf. A000720, A119524 (measure of composites), A010051, A113829.
Sequence in context: A143531 A019865 A198993 * A181164 A154212 A155035
Adjacent sequences: A119520 A119521 A119522 * A119524 A119525 A119526
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KEYWORD
| nonn,cons
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AUTHOR
| Roger L. Bagula (rlbagultftn(AT)yahoo.com), May 27 2006
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EXTENSIONS
| More terms from Peter Pein (petsie(AT)dordos.net), May 31 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2006
Corrected use of PrimePi in the first comment line - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2010
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