cp's OEIS Frontend

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.

%I A369823 #12 Feb 05 2024 02:39:03
%S A369823 0,1,4096,0,531441,46656,0,15625,729,1,4096,4096,1,4096,46656,46656,
%T A369823 15625,46656,0,1,15625,46656,64,15625,117649,64,531441,1,4096,0,
%U A369823 531441,46656,4096,0,531441,46656,1,4096,0,531441,46656,4096,46656,46656,15625,46656,4096,46656,46656,15625,46656,1
%N 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.
%C A369823 S is the lexicographycally earliest sequence of nonnegative integers with this property.
%H A369823 Eric 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 A369823 a(1) = 0, which raised at the 6th power gives 0
%e A369823 a(2) = 1, which raised at the 6th power gives 1
%e A369823 a(3) = 4096
%e A369823      1st digit is 4, which raised at the 6th power gives 4096
%e A369823      2nd digit is 0, which raised at the 6th power gives 0
%e A369823      3rd digit is 9, which raised at the 6th power gives 531441
%e A369823      4th digit is 6, which raised at the 6th power gives 46656
%e A369823 Etc. We see that the above last column reproduces S.
%t A369823 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 *)
%Y A369823 Cf. A369603, A369604, A369798, A369824, A001014.
%K A369823 base,nonn
%O A369823 1,3
%A A369823 _Eric Angelini_, Feb 02 2024