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Total number of positive integers below 10^n requiring 2 positive biquadrates in their representation as sum of biquadrates.
19

%I #16 Feb 11 2024 23:45:02

%S 1,5,14,43,143,460,1467,4613,14629,46341,146545,463344,1465658,

%T 4634967,14657277,46350371

%N Total number of positive integers below 10^n requiring 2 positive biquadrates in their representation as sum of biquadrates.

%C A114322(n) + a(n) + A186651(n) + A186653(n) + A186655(n) + A186657(n) + A186659(n) + A186661(n) + A186663(n) + A186665(n) + A186667(n) + A186669(n) + A186671(n) + A186673(n) + A186675(n) + A186677(n) + A186680(n) + A186682(n) + A186684(n) = A002283(n).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WaringsProblem.html">Waring's Problem</a>.

%p isbiquadrate:=proc(n) type(root(n,4),posint); end:

%p isA003336:=proc(n) local x,y4; if isbiquadrate(n) then false; else for x from 1 do y4:=n-x^4; if y4<x^4 then return false; elif isbiquadrate(y4) then return true; fi; od; fi; end:

%p a:=proc(n) local i,k; i:=0; for k from 2 to 10^n-1 do if isA003336(k) then i:=i+1; fi; od: return(i); end: for n from 1 do print(a(n)); od;

%Y Cf. A003336.

%K nonn

%O 1,2

%A _Martin Renner_, Feb 25 2011

%E a(6) from _Martin Renner_, Feb 26 2011

%E a(7)-a(16) from _Lars Blomberg_, May 08 2011