%I #16 Apr 02 2021 17:56:41
%S 0,1,3,16,5,256,7,1296,9,4096,11,10000,13,20736,15,38416,81,18,83521,
%T 20,130321,22,194481,24,279841,26,390625,28,531441,30,707281,32,
%U 923521,34,1185921,36,1500625,38,1874161,40,2313441,42,2825761,44,3418801,46
%N Earliest sequence with a(a(n)) = n^4.
%H T. D. Noe, <a href="/A054793/b054793.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Aa#aan">Index entries for sequences of the a(a(n)) = 2n family</a>
%F if n is a 4th power then a(n)=a(n^(1/4))^4, otherwise if the difference between n and the highest 4th power less than n is odd then a(n)=n+1, otherwise a(n)=(n-1)^4.
%t a[n_] := a[n] = Which[r = n^(1/4); IntegerQ[r], a[r]^4, OddQ[n - Floor[r]^4], n+1, True, (n-1)^4]; a[0]=0; a[1]=1; Table[a[n], {n, 0, 45}] (* _Jean-François Alcover_, Aug 07 2012, after formula *)
%o (Python)
%o from sympy import integer_nthroot
%o def A054793(n):
%o a, b = integer_nthroot(n,4)
%o return n if n <= 1 else A054793(a)**4 if b else n+1 if (n-a**4) % 2 else (n-1)**4 # _Chai Wah Wu_, Apr 02 2021
%Y Cf. A000290, A007379.
%K nonn,nice
%O 0,3
%A _Henry Bottomley_, Apr 27 2000