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, 100224898, 316939574, 1002254727, 3169403764, 10022551343, 31694105527, 100225585696, 316941129401, 1002255999950, 3169411795537, 10022560398983, 31694119013758

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..28.

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

a(17)-a(24) from Martin Fuller, Jan 01 2026

a(25)-a(28) from A003824 by Martin Fuller, Feb 01 2026

Status

approved