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Decimal expansion of 7^(1/4) - 5^(1/4).
9

%I #21 Aug 21 2023 12:21:10

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

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

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

%N Decimal expansion of 7^(1/4) - 5^(1/4).

%C Decimal expansion of maximal value of function beta(n) = sigma(n)^(1/n) - (n+1)^(1/n) for n = 4, where beta(n) is called the beta-deviation from primality of number n (see A234520). Lim_n->infinity beta(n) = 0.

%C An algebraic integer with degree 16 and minimal polynomial x^16 - 48x^12 - 3896x^8 - 53952x^4 + 16. - _Charles R Greathouse IV_, Apr 25 2016

%H <a href="/index/Al#algebraic_16">Index entries for algebraic numbers, degree 16</a>

%F Equals A011005-A011003.

%e 0.13122778047656520129933335...

%t RealDigits[N[7^(1/4)-5^(1/4), 100]][[1]] (* _Georg Fischer_, Apr 04 2020 *)

%o (PARI) 7^(1/4) - 5^(1/4) \\ _Charles R Greathouse IV_, Apr 25 2016

%Y Cf. A234515, A234516, A234517, A234518, A234519, A234520, A234521, A234523, A234524.

%K nonn,cons

%O 0,2

%A _Jaroslav Krizek_, Jan 14 2014

%E a(97) corrected by _Georg Fischer_, Apr 04 2020