cp's OEIS Frontend

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.

%I A369824 #12 Feb 05 2024 02:38:39
%S A369824 0,1,256,390625,1679616,6561,43046721,0,1679616,256,390625,1,1679616,
%T A369824 5764801,43046721,1679616,1,1679616,1679616,390625,1679616,1,65536,
%U A369824 6561,0,65536,1679616,5764801,256,1,0,1,1679616,5764801,43046721,1679616,1,1679616,256,390625,1679616,6561,43046721
%N 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.
%C A369824 S is the lexicographycally earliest sequence of nonnegative integers with this property.
%H A369824 Éric Angelini and Jean-Marc Falcoz, <a href="https://cinquantesignes.blogspot.com/2024/02/boomerang-sequences.html">Boomerang sequences</a>, Personal blog, Feb 1st 2024.
%e A369824 a(1) = 0, which raised at the 8th power gives 0
%e A369824 a(2) = 1, which raised at the 8th power gives 1
%e A369824 a(3) = 256
%e A369824      1st digit is 2, which raised at the 8th power gives 256
%e A369824      2nd digit is 5, which raised at the 8th power gives 390625
%e A369824      3rd digit is 6, which raised at the 8th power gives 1679616
%e A369824 Etc. We see that the above last column reproduces S.
%t A369824 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 *)
%Y A369824 Cf. A369603, A369604, A369798, A369823, A001014, A001016.
%K A369824 base,nonn
%O A369824 1,3
%A A369824 _Eric Angelini_, Feb 02 2024