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%I #22 Apr 12 2022 04:23:21
%S 1,109,113,114,199,200,201,241,242,271,277,281,282,283,284,285,286,
%T 287,288,289,293,294,295,313,317,318,319,443,444,445,449,450,451,457,
%U 458,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476
%N 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.
%C Panaitopol (1999) proved that all the numbers >= 1429 are in this sequence. - _Amiram Eldar_, Apr 12 2022
%H Reinhard Zumkeller, <a href="/A051046/b051046.txt">Table of n, a(n) for n = 1..2500</a>
%H Laurenţiu Panaitopol, <a href="http://dx.doi.org/10.7153/mia-02-29">Several Approximations of pi(x)</a>, Math. Ineq. Appl., Vol. 2, No. 3 (1999), pp. 317-324.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeCountingFunction.html">Prime Counting Function</a>.
%t ppQ[n_]:=PrimePi[n]-n/(HarmonicNumber[n]-3/2)>0; Select[Range[500],ppQ] (* _Harvey P. Dale_, Feb 16 2012 *)
%o (Haskell)
%o a051046 n = a051046_list !! (n-1)
%o a051046_list = filter
%o (\x -> fromIntegral (a000720 x) > hs !! (x - 1)) [1..]
%o where hs = zipWith (/)
%o [1..] $ map (subtract 1.5) $ scanl1 (+) $ map (1 /) [1..]
%o -- _Reinhard Zumkeller_, Mar 20 2014
%Y Cf. A000720, A001008, A002805.
%K nonn
%O 1,2
%A _Eric W. Weisstein_
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