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A237684 a(n) = floor(n*prime(n) / Sum_{i<=n} prime(i)). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,7
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.
LINKS
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.
FORMULA
a(n) = floor(A033286(n) / A007504(n)).
EXAMPLE
For n=8: a(8) = floor(8*Prime(8) / Sum_i<=8 (Prime(i)) = 8*19 / 77 = 1.
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 *)
CROSSREFS
Sequence in context: A297784 A043568 A043543 * A130634 A274828 A364136
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Feb 21 2014
STATUS
approved

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Last modified July 18 10:00 EDT 2024. Contains 374378 sequences. (Running on oeis4.)