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

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 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.
		

Links

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

Crossrefs

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

Programs

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 *)