login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numbers that can be represented as j^4 + k^4, with 0 < j < k, in exactly one way.
11

%I #19 Feb 15 2023 18:48:33

%S 17,82,97,257,272,337,626,641,706,881,1297,1312,1377,1552,1921,2402,

%T 2417,2482,2657,3026,3697,4097,4112,4177,4352,4721,5392,6497,6562,

%U 6577,6642,6817,7186,7857,8962,10001,10016,10081,10256,10625,10657,11296

%N Numbers that can be represented as j^4 + k^4, with 0 < j < k, in exactly one way.

%H Robert Israel, <a href="/A088687/b088687.txt">Table of n, a(n) for n = 1..4500</a>

%e 17 = 1^4 + 2^4.

%e 635318657 = 133^4 + 134^4 is absent because it is also 59^4 + 158^4 (see A046881, A230562)

%p N:= 2*10^4: # for terms <= N

%p V:= Vector(N):

%p for j from 1 while 2*j^4 < N do

%p for k from j+1 do

%p r:= j^4 + k^4;

%p if r > N then break fi;

%p V[r]:= V[r]+1;

%p od od:

%p select(t -> V[t] = 1, [$1..N]); $ _Robert Israel_, Dec 15 2019

%t lst={};Do[Do[x=a^4;Do[y=b^4;If[x+y==n,AppendTo[lst,n]],{b,Floor[(n-x)^(1/4)],a+1,-1}],{a,Floor[n^(1/4)],1,-1}],{n,4*7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 22 2009 *)

%o (PARI) powers2(m1,m2,p1) = { for(k=m1,m2, a=powers(k,p1); if(a==1,print1(k",")) ); } powers(n,p) = { z1=0; z2=0; c=0; cr = floor(n^(1/p)+1); for(x=1,cr, for(y=x+1,cr, z1=x^p+y^p; if(z1 == n,c++); ); ); return(c) }

%Y Cf. A003336, A088728.

%K nonn

%O 1,1

%A _Cino Hilliard_, Nov 22 2003

%E Edited by _Don Reble_, May 03 2006