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%I #30 Jul 29 2022 16:52:58
%S 3,7,13,23,31,47,61,79,97,113,139,167,193,223,251,283,317,359,397,439,
%T 479,523,571,619,673,727,773,839,887,953,1021,1087,1153,1223,1291,
%U 1367,1439,1511,1597,1669,1759,1847,1933,2017,2113,2207,2297,2399,2477,2593
%N Largest prime < n^2.
%C Suggested by Legendre's conjecture (still open) that there is always a prime between n^2 and (n+1)^2.
%C Legendre's conjecture is equivalent to a(n) > (n-1)^2. - _John W. Nicholson_, Dec 11 2013
%D J. R. Goldman, The Queen of Mathematics, 1998, p. 82.
%H T. D. Noe, <a href="/A053001/b053001.txt">Table of n, a(n) for n=2..1000</a>
%F a(n) = A007917(A000290(n)). - _Reinhard Zumkeller_, Jun 07 2015
%p [seq(prevprime(i^2),i=2..100)];
%t Table[Prime[PrimePi[n^2]], {n, 2, 60}] (* _Stefan Steinerberger_, Apr 01 2006 *)
%t Table[NextPrime[n^2, -1], {n, 2, 60}] (* _Jean-François Alcover_, Oct 14 2013 *)
%o (PARI) a(n) = precprime(n^2) \\ _Michel Marcus_, Oct 14 2013
%o (Haskell)
%o a053001 = a007917 . a000290 -- _Reinhard Zumkeller_, Jun 07 2015
%o (Python)
%o from sympy import prevprime
%o def a(n): return prevprime(n*n)
%o print([a(n) for n in range(2, 52)]) # _Michael S. Branicky_, Jul 29 2022
%Y Cf. A007491, A053000, A014085.
%Y Cf. A007917, A000290.
%K nonn,easy,nice
%O 2,1
%A _N. J. A. Sloane_, Feb 21 2000
%E More terms from _James A. Sellers_, Feb 22 2000
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