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A051046
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Numbers k for which pi(k) > k/(H_k - 3/2), where pi is the prime-counting function and H_k is the k-th harmonic number.
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1
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1, 109, 113, 114, 199, 200, 201, 241, 242, 271, 277, 281, 282, 283, 284, 285, 286, 287, 288, 289, 293, 294, 295, 313, 317, 318, 319, 443, 444, 445, 449, 450, 451, 457, 458, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Panaitopol (1999) proved that all the numbers >= 1429 are in this sequence. - Amiram Eldar, Apr 12 2022
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LINKS
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MATHEMATICA
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ppQ[n_]:=PrimePi[n]-n/(HarmonicNumber[n]-3/2)>0; Select[Range[500], ppQ] (* Harvey P. Dale, Feb 16 2012 *)
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PROG
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(Haskell)
a051046 n = a051046_list !! (n-1)
a051046_list = filter
(\x -> fromIntegral (a000720 x) > hs !! (x - 1)) [1..]
where hs = zipWith (/)
[1..] $ map (subtract 1.5) $ scanl1 (+) $ map (1 /) [1..]
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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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