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Search: id:A117490
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| A117490 |
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Number of primes between n and n^2 (with n and n^2 excluded). |
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3
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| 0, 1, 2, 4, 6, 8, 11, 14, 18, 21, 25, 29, 33, 38, 42, 48, 54, 59, 64, 70, 77, 84, 90, 96, 105, 113, 120, 128, 136, 144, 151, 161, 170, 180, 189, 199, 207, 216, 228, 239, 250, 261, 269, 281, 292, 305, 314, 327, 342, 352, 363, 378, 393, 405, 418, 429, 441, 458, 470
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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A famous Japanese mathematics book states that this sequence is nonzero (for n>1) if the Riemann Hypothesis is true, but this statement seems to be false.
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FORMULA
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a(n) = pi(n^2)-pi(n), cf. A000720.
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EXAMPLE
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For n=5: between 5+1 = 6 and 5^2-1 = 24 there are the following six primes: 7, 11, 13, 17, 19, 23.
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MAPLE
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P:=proc(n) local i, j, np; for i from 1 by 1 to n do np:=0; for j from i+1 by 1 to i^2-1 do if isprime(j) then np:=np+1; fi; od; print(np); od; end: P(100);
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MATHEMATICA
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f[n_] := PrimePi[n^2 - 1] - PrimePi[n]; Array[f, 59] (from Robert G. Wilson v (rgwv(at)rgwv.com), Apr 06 2006)
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CROSSREFS
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Cf. A014085, A060715, A117491.
Sequence in context: A092777 A006463 A060655 this_sequence A032514 A011858 A084627
Adjacent sequences: A117487 A117488 A117489 this_sequence A117491 A117492 A117493
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KEYWORD
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easy,nonn
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AUTHOR
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Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Mar 22 2006
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