A124478 a(n) = prime(n) - floor((2/n)*Sum_{i=1..n} prime(i)).

-2, -2, -1, -1, 0, 0, 1, 0, 1, 4, 2, 5, 5, 3, 4, 6, 8, 6, 8, 8, 6, 8, 7, 9, 13, 12, 10, 10, 7, 7, 17, 16, 17, 14, 19, 17, 18, 19, 18, 19, 20, 17, 22, 19, 18, 16, 23, 29, 28, 25, 24, 25, 21, 26, 27, 28, 28, 25, 26, 25, 22, 27, 35, 34, 30, 29, 37, 38, 42, 38, 37, 37, 40, 40, 40, 39, 39, 41, 40, 42

Offset

1,1

Comments

Robert Mandl conjectured and Rosser and Schoenfeld proved that prime(n)/2 > (Sum_{i=1..n} prime(i))/n for n >= 9 (implying that a(n) > 0 for n >= 9).

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

C. Axler, On a Sequence involving Prime Numbers, J. Int. Seq. 18 (2015) # 15.7.6

Christian Axler, New bounds for the sum of the first n prime numbers, arXiv:1606.06874 [math.NT], 2016.

Pierre Dusart, Autour de la fonction qui compte le nombre de nombres premiers, Thèse, Université de Limoges, France, (1998), see Section 1.9.

M. Hassani, A Remark on the Mandl's Inequality, arXiv:math/0606765 [math.NT], 2006.

J. Barkley Rosser and Lowell Schoenfeld, Sharper bounds for the Chebyshev functions theta(x) and psi(x), Collection of articles dedicated to Derrick Henry Lehmer on the occasion of his seventieth birthday. Math. Comp. 29 (1975), 243-269.

Mathematica

Table[Prime[n] - Floor[(2/n)*Sum[Prime[i], {i, n}]], {n, 100}] (* Michael De Vlieger, Jan 31 2015 *)

Crossrefs

Sequence in context: A054924 A370167 A046751 * A030353 A089617 A359217

Adjacent sequences: A124475 A124476 A124477 * A124479 A124480 A124481

Keyword

sign

Author

N. J. A. Sloane, Dec 17 2006

Status

approved