A369824 S is a "boomerang sequence": replace each digit d of S by its eighth power: the sequence S remains identical to itself if we follow each result with a comma.

0, 1, 256, 390625, 1679616, 6561, 43046721, 0, 1679616, 256, 390625, 1, 1679616, 5764801, 43046721, 1679616, 1, 1679616, 1679616, 390625, 1679616, 1, 65536, 6561, 0, 65536, 1679616, 5764801, 256, 1, 0, 1, 1679616, 5764801, 43046721, 1679616, 1, 1679616, 256, 390625, 1679616, 6561, 43046721

Offset

1,3

Comments

S is the lexicographycally earliest sequence of nonnegative integers with this property.

Links

Table of n, a(n) for n=1..43.

Éric Angelini and Jean-Marc Falcoz, Boomerang sequences, Personal blog, Feb 1st 2024.

Example

a(1) = 0, which raised at the 8th power gives 0
a(2) = 1, which raised at the 8th power gives 1
a(3) = 256
     1st digit is 2, which raised at the 8th power gives 256
     2nd digit is 5, which raised at the 8th power gives 390625
     3rd digit is 6, which raised at the 8th power gives 1679616
Etc. We see that the above last column reproduces S.

Mathematica

a[1]=0; a[2]=1; a[3]=2^8; a[n_]:=a[n]=Flatten[IntegerDigits/@Array[a, n-1]][[n]]^8; Array[a, 43] (* Giorgos Kalogeropoulos, Feb 04 2024 *)

Crossrefs

Cf. A369603, A369604, A369798, A369823, A001014, A001016.

Sequence in context: A220302 A013833 A100636 * A016796 A018877 A283803

Adjacent sequences: A369821 A369822 A369823 * A369825 A369826 A369827

Keyword

base,nonn

Author

Eric Angelini, Feb 02 2024

Status

approved