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A053001 Largest prime < n^2.

%I A053001 #31 Jul 02 2025 16:01:59
%S A053001 3,7,13,23,31,47,61,79,97,113,139,167,193,223,251,283,317,359,397,439,
%T A053001 479,523,571,619,673,727,773,839,887,953,1021,1087,1153,1223,1291,
%U A053001 1367,1439,1511,1597,1669,1759,1847,1933,2017,2113,2207,2297,2399,2477,2593
%N A053001 Largest prime < n^2.
%C A053001 Suggested by Legendre's conjecture (still open) that there is always a prime between n^2 and (n+1)^2.
%C A053001 Legendre's conjecture is equivalent to a(n) > (n-1)^2. - _John W. Nicholson_, Dec 11 2013
%D A053001 J. R. Goldman, The Queen of Mathematics, 1998, p. 82.
%H A053001 T. D. Noe, <a href="/A053001/b053001.txt">Table of n, a(n) for n=2..1000</a>
%F A053001 a(n) = A007917(A000290(n)). - _Reinhard Zumkeller_, Jun 07 2015
%p A053001 [seq(prevprime(i^2),i=2..100)];
%t A053001 Table[Prime[PrimePi[n^2]], {n, 2, 60}] (* _Stefan Steinerberger_, Apr 01 2006 *)
%t A053001 Table[NextPrime[n^2, -1], {n, 2, 60}] (* _Jean-François Alcover_, Oct 14 2013 *)
%o A053001 (PARI) a(n) = precprime(n^2) \\ _Michel Marcus_, Oct 14 2013
%o A053001 (Haskell)
%o A053001 a053001 = a007917 . a000290  -- _Reinhard Zumkeller_, Jun 07 2015
%o A053001 (Python)
%o A053001 from sympy import prevprime
%o A053001 def a(n):  return prevprime(n*n)
%o A053001 print([a(n) for n in range(2, 52)]) # _Michael S. Branicky_, Jul 29 2022
%Y A053001 Cf. A007491, A053000, A014085.
%Y A053001 Cf. A007917, A000290.
%K A053001 nonn,easy,nice
%O A053001 2,1
%A A053001 _N. J. A. Sloane_, Feb 21 2000
%E A053001 More terms from _James Sellers_, Feb 22 2000