OFFSET
1,3
COMMENTS
Apart from 0, 1, 2, there are no three consecutive terms up to 10^16. The first two consecutive terms not of the form n^4, n^4+1 are 3502321 = 25^4 + 42^4, 3502322 = 17^4 + 43^4. - Charles R Greathouse IV, Oct 17 2017
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
FORMULA
Call f(x) the number of terms if this sequence up to x. Then x^(7/16) << f(x) << x^(1/2); in other words, n^2 << a(n) << n^(16/7). The upper bound becomes O(n^2) if A230562 is finite. - Charles R Greathouse IV, Jul 12 2024
MATHEMATICA
Reap[For[n = 0, n < 10000, n++, If[MatchQ[ PowersRepresentations[n, 2, 4], {{_, _}, ___}], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Oct 30 2017 *)
PROG
(Haskell)
a004831 n = a004831_list !! (n-1)
a004831_list = [x ^ 4 + y ^ 4 | x <- [0..], y <- [0..x]]
-- Reinhard Zumkeller, Jul 15 2013
(PARI) is(n)=#thue(thueinit(z^4+1), n) \\ Ralf Stephan, Oct 18 2013
(PARI) list(lim)=my(v=List(), t); for(m=0, sqrtnint(lim\=1, 4), for(n=0, min(sqrtnint(lim-m^4, 4), m), listput(v, n^4+m^4))); Set(v) \\ Charles R Greathouse IV, Sep 28 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved