A011443 - OEIS

%I #24 Sep 08 2022 08:44:37

%S 1,1,4,1,5,8,6,4,4,0,6,3,2,1,6,3,4,2,4,4,6,0,8,2,9,3,6,5,1,9,7,2,7,7,

%T 6,7,6,1,6,0,8,5,1,6,8,3,2,0,5,5,4,1,4,6,9,1,1,6,8,3,1,0,3,8,7,0,5,8,

%U 0,3,7,6,1,6,5,9,9,5,3,2,5,8,9,1,2,4,8,4,3,4,4,6,5,0,9,6,7,7,2

%N Decimal expansion of 24th root of 24.

%C Sanna shows that the number of inequivalent arithmetic expressions of n is this constant raised to the power of n + O(sqrt(n)). "Arithmetic expressions", in this context, are formulas with 1s, parentheses, addition, and multiplication, disallowing multiplication by 1. - _Charles R Greathouse IV_, Jan 27 2016

%H Ivan Panchenko, <a href="/A011443/b011443.txt">Table of n, a(n) for n = 1..1000</a>

%H Carlo Sanna, <a href="http://dx.doi.org/10.1142/S1793042115500591">On the number of arithmetic formulas</a>, Int. J. Number Theory 11 (2015), p. 1099.

%t RealDigits[24^(1/24), 10, 90][[1]] (* _Bruno Berselli_, Feb 03 2016 *)

%o (PARI) sqrtn(24,24) \\ _Charles R Greathouse IV_, Jan 27 2016

%o (Magma) 24^(1/24); // _Vincenzo Librandi_, Feb 03 2016

%K nonn,cons

%O 1,3

%A _N. J. A. Sloane_