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A051046 n for which pi(n) > n/(H_n-3/2), where pi is the prime-counting function and H_n is the n-th harmonic number. 1
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)
OFFSET

1,2

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..2500

E. W. Weisstein, MathWorld: Harmonic Number

Eric Weisstein's World of Mathematics, Prime Counting Function

MATHEMATICA

ppQ[n_]:=PrimePi[n]-n/(HarmonicNumber[n]-3/2)>0; Select[Range[500], ppQ] (* Harvey P. Dale, Feb 16 2012 *)

PROG

(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..]

-- Reinhard Zumkeller, Mar 20 2014

CROSSREFS

Cf. A000720.

Sequence in context: A253438 A263194 A231701 * A196667 A196673 A159027

Adjacent sequences:  A051043 A051044 A051045 * A051047 A051048 A051049

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified December 10 00:24 EST 2016. Contains 278993 sequences.