A216071 - OEIS

%I #23 Sep 16 2022 12:52:36

%S 5,11,71

%N Brocard's problem: positive integers m such that m^2 = n! + 1 for some n.

%C See A085692 and A146968 for links, references and comments. - _M. F. Hasler_, Nov 20 2018

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Brocard%27s_problem">Brocard's problem</a>

%F a(n) = A000196(A085692(n)) = A000196(A038507(A146968(n))) where A000196 = sqrt and A038507(n) = n! + 1. - _M. F. Hasler_, Nov 20 2018

%t Sqrt[#!+1]&/@Select[Range[1000],IntegerQ[Sqrt[#!+1]]&] (* _Harvey P. Dale_, Sep 29 2012 *)

%o (PARI) apply( sqrtint, A085692) \\ _M. F. Hasler_, Nov 20 2018

%o (PARI) select( is_A216071(m)=m^2==A084558(m^2)!+1, [0..99]) \\ _M. F. Hasler_, Nov 20 2018

%Y A085692, A146968, A216071 are all essentially the same sequence. - _N. J. A. Sloane_, Sep 01 2012

%K nonn,hard,bref

%O 1,1

%A _V. Raman_, Sep 01 2012