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A237684
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a(n) = floor(n*prime(n) / Sum_{i<=n} prime(i)).
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1
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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
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OFFSET
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1,7
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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For n=8: a(8) = floor(8*Prime(8) / Sum_i<=8 (Prime(i)) = 8*19 / 77 = 1.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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