A186650 Total number of n-digit numbers requiring 2 positive biquadrates in their representation as sum of biquadrates.

1, 4, 9, 29, 100, 317, 1007, 3146, 10016, 31712, 100204, 316799, 1002314, 3169309, 10022310, 31693094

Offset

1,2

Comments

A102831(n) + a(n) + A186652(n) + A186654(n) + A186656(n) + A186658(n) + A186660(n) + A186662(n) + A186664(n) + A186666(n) + A186668(n) + A186670(n) + A186672(n) + A186674(n) + A186676(n) + A186678(n) + A186681(n) + A186683(n) + A186685(n) = A052268(n), for n>1.

Links

Table of n, a(n) for n=1..16.

Eric Weisstein's World of Mathematics, Waring's Problem.

Formula

a(n) = A186649(n)-A186649(n-1).

Maple

isbiquadrate:=proc(n) type(root(n, 4), posint); end:
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:
a:=proc(n) local i, k; i:=0; for k from 10^(n-1) 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;

Crossrefs

Cf. A003336, A186649.

Sequence in context: A127768 A231255 A241393 * A091658 A297960 A295910

Adjacent sequences: A186647 A186648 A186649 * A186651 A186652 A186653

Keyword

nonn,base,more

Author

Martin Renner, Feb 25 2011

Extensions

a(6) from Martin Renner, Feb 26 2011

a(7)-a(16) from Giovanni Resta, Apr 29 2016

Status

approved