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%I #18 Jun 18 2023 01:50:11
%S 1,3,9,3,0,9,1,5,4,5,3,8,5,7,1,0,5,9,2,2,2,6,1,4,0,7,8,3,2,9,4,4,6,1,
%T 9,4,0,9,8,1,1,6,1,3,1,7,8,4,5,3,5,6,9,6,0,8,0,2,9,2,4,8,0,9,7,6,4,2,
%U 7,6,9,9,0,2,8,4,6,5,3,0,5,9,3,1,2,2,9,9,6,7,9,9,4,1,3,7,9,2,2,9
%N Decimal expansion of x such that x^(x+3) = x^x + x^3.
%e 1.393091545385710592226140783294461940981161317845356960802924...
%t RealDigits[x /. FindRoot[x^(x + 3) == x^x + x^3, {x, 3/2}, WorkingPrecision -> 120]][[1]] (* _Amiram Eldar_, Jun 18 2023 *)
%o (PARI) solve(x=1,2,x^(x+3)-x^x-x^3)
%Y Cf. A008789 (n^(n+3)), A316295 (similar, with 2 instead of 3).
%K nonn,cons
%O 1,2
%A _Patrick C. Schneider_, Aug 18 2018
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