A054793 Earliest sequence with a(a(n)) = n^4.

0, 1, 3, 16, 5, 256, 7, 1296, 9, 4096, 11, 10000, 13, 20736, 15, 38416, 81, 18, 83521, 20, 130321, 22, 194481, 24, 279841, 26, 390625, 28, 531441, 30, 707281, 32, 923521, 34, 1185921, 36, 1500625, 38, 1874161, 40, 2313441, 42, 2825761, 44, 3418801, 46

Offset: 0

Author

Henry Bottomley, Apr 27 2000

Keywords

• nonn
• nice

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for sequences of the a(a(n)) = 2n family

Crossrefs

Cf. A000290, A007379.

Programs

Mathematica

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 *)

Python

from sympy import integer_nthroot
def A054793(n):
    a, b = integer_nthroot(n,4)
    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

Formula

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.