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.
Numbers n such that n and 2*n are both in A003336. - Michel Marcus, Feb 25 2017
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
Izadi & Nabardi construct a collection of elliptic curves of rank >= 5 using (essentially) terms of this sequence. - Charles R Greathouse IV, Jul 13 2024
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..513 (terms < 10^16)
Farzali Izadi and Kamran Nabardi, A Family of Elliptic Curves With Rank >= 5, arXiv preprint (2015). arXiv:1501.03809 [math.NT]
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
Altug Alkan and Thomas Ordowski, Feb 25 2017
EXTENSIONS
a(10)-a(22) from Giovanni Resta, Feb 25 2017
STATUS
approved