A369823 S is a "boomerang sequence": replace each digit d of S by its sixth power: the sequence S remains identical to itself if we follow each result with a comma.

0, 1, 4096, 0, 531441, 46656, 0, 15625, 729, 1, 4096, 4096, 1, 4096, 46656, 46656, 15625, 46656, 0, 1, 15625, 46656, 64, 15625, 117649, 64, 531441, 1, 4096, 0, 531441, 46656, 4096, 0, 531441, 46656, 1, 4096, 0, 531441, 46656, 4096, 46656, 46656, 15625, 46656, 4096, 46656, 46656, 15625, 46656, 1

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..52.

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

Example

a(1) = 0, which raised at the 6th power gives 0
a(2) = 1, which raised at the 6th power gives 1
a(3) = 4096
     1st digit is 4, which raised at the 6th power gives 4096
     2nd digit is 0, which raised at the 6th power gives 0
     3rd digit is 9, which raised at the 6th power gives 531441
     4th digit is 6, which raised at the 6th power gives 46656
Etc. We see that the above last column reproduces S.

Mathematica

a[1]=0; a[2]=1; a[3]=4^6; a[n_]:=a[n]=Flatten[IntegerDigits/@Array[a, n-1]][[n]]^6; Array[a, 52] (* Giorgos Kalogeropoulos, Feb 04 2024 *)

Crossrefs

Cf. A369603, A369604, A369798, A369824, A001014.

Sequence in context: A076154 A182685 A182686 * A176768 A223601 A186490

Adjacent sequences: A369820 A369821 A369822 * A369824 A369825 A369826

Keyword

base,nonn

Author

Eric Angelini, Feb 02 2024

Status

approved