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