A098990 Decimal expansion of Sum_{n>=1} prime(n)/(2^n).
3, 6, 7, 4, 6, 4, 3, 9, 6, 6, 0, 1, 1, 3, 2, 8, 7, 7, 8, 9, 9, 5, 6, 7, 6, 3, 0, 9, 0, 8, 4, 0, 2, 9, 4, 1, 1, 6, 7, 7, 7, 9, 7, 5, 8, 8, 7, 7, 9, 4, 3, 7, 3, 2, 8, 3, 1, 2, 2, 0, 5, 2, 2, 0, 1, 7, 6, 3, 7, 9, 8, 6, 7, 0, 4, 4, 8, 2, 8, 3, 6, 0, 4, 1, 7, 4, 5, 4, 7, 6, 4, 5, 7, 8, 8, 0, 1, 9, 0, 1, 1, 3, 7, 5, 2
Offset: 1
Examples
3.6746439660113287789956763090840294116777975887794373283122052201763...
References
- Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.2.1, p. 96.
Links
- Peter J. Cho and Henry H. Kim, The average of the smallest prime in a conjugacy class, International Mathematics Research Notices, Vol. 2020, No. 6 (2020), pp. 1718-1747, arXiv preprint, arXiv:1601.03012 [math.NT], 2016.
- Paul Erdős, Remarks on number theory. I., Mat. Lapok, Vol. 12 (1961), pp. 10-17; Math. Rev. 26 #2410.
- S. R. Finch, Average least nonresidues, December 4, 2013. [Cached copy, with permission of the author]
- Paul Pollack, The average least quadratic nonresidue modulo m and other variations on a theme of Erdős, J. Number Theory, Vol. 132, No. 6 (2012), pp. 1185-1202, alternative link.
Programs
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Maple
f:=N->sum(ithprime(n)/2^n,n=1..N); evalf[106](f(500)); evalf[106](f(1000));
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Mathematica
RealDigits[Sum[Prime[i]/2^i,{i,1000}],10,120][[1]] (* Harvey P. Dale, Apr 10 2012 *) -
PARI
suminf(k=1, prime(k)/2^k) \\ Michel Marcus, Jan 13 2016
Formula
Equals Sum_{n>=1} prime(n)/2^n.
Equals 2 plus the constant in A098882. - R. J. Mathar, Sep 02 2008
Equals lim_{n->oo} (1/n) * Sum_{k=1..n} A053760(k). - Amiram Eldar, Oct 29 2020
Comments