A237684 a(n) = floor(n*prime(n) / Sum_{i<=n} prime(i)).

1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Author

Jaroslav Krizek, Feb 21 2014

Keywords

• nonn

Comments

a(n) = 1 for n = 8 and 1 <= n <= 6.

a(n) = 2 for n = 7 and 9 <= n < 10^11 (verified terms).

Conjectures:

(1): a(n) = 1 or 2 for all n.

(2): sequence of numbers n sorted by decreasing values of function f(n) = n*prime(n) / Sum_{i<=n} prime(i): 48, 35, 31, 25, 17, 49, 33, 69, 32, 26, 43, 38, 12, 63, 102, 67, 68, 37, ... The last term of this sequence is 1.

(3): maximal value of function f(n) is for n = 48: f(48) = 10704/4661 = 2.29650289637416...

(4): minimal value of function f(n) is for n = 1: f(1) = 1.

Examples

			a(8) = floor(8*prime(8) / Sum_{i<=8} prime(i)) = floor(8*19 / 77) = 1.
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..87
• Manuel Kauers and Christoph Koutschan, Some D-finite and some Possibly D-finite Sequences in the OEIS, arXiv:2303.02793 [cs.SC], 2023, p. 4.

Crossrefs

Cf. A007504, A033286.

Programs

Mathematica

Block[{$MaxExtraPrecision = 1000, a, t = 0, nn = 120}, Do[(t += #; Set[a[i], Floor[i*#/t]]) &[Prime[i]], {i, nn}]; Array[a, nn] ] (* Michael De Vlieger, Mar 10 2023 *)

Formula

a(n) = floor(A033286(n) / A007504(n)).