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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.
5
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
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
KEYWORD
base,nonn
AUTHOR
Eric Angelini, Feb 02 2024
STATUS
approved