|
|
A282948
|
|
Numbers n such that (u^4 + v^4)/2 = x^4 + y^4 = n has a solution in positive integers u,v,x,y.
|
|
1
|
|
|
162401, 2598416, 13154481, 41574656, 101500625, 210471696, 389924801, 665194496, 1065512961, 1624010000, 2377713041, 3367547136, 4638334961, 6238796816, 8221550625, 10643111936, 13563893921, 17048207376, 21164260721, 25984160000, 31583908881, 38043408656
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
All terms are composite.
If n is in this sequence, then n*k^4 with k > 0 is in this sequence.
The first term which is not a multiple of a(1) is a(84) = 8051889328801. - Giovanni Resta, Feb 25 2017
Based on Giovanni Resta's b-file, the squarefree terms are 162401, 8051889328801, 9305528350081, 16778006844241, .... - Altug Alkan, Feb 26 2017
|
|
LINKS
|
|
|
EXAMPLE
|
(19^4 + 21^4)/2 = 7^4 + 20^4 = 162401.
|
|
PROG
|
(PARI) isA003336(n) = for(k=1, sqrtnint(n\2, 4), ispower(n-k^4, 4) && return(1));
is(n) = isA003336(n) && isA003336(2*n);
(PARI) T=thueinit('x^4+1, 1);
has(n)=#thue(T, n)>0 && !issquare(n)
list(lim)=my(v=List(), x4, t); for(x=1, sqrtnint(lim\=1, 4), x4=x^4; for(y=1, min(sqrtnint(lim-x4, 4), x), t=x4+y^4; if(has(2*t), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 26 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|