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

Author

Eric Angelini, Feb 02 2024

Keywords

• base
• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)