This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A338129 #17 Jan 12 2022 15:01:02
%S A338129 1,3,5,7,9,13,15,17,25,31,33,41,49,57,63,65,81,97,113,127,129,145,161,
%T A338129 177,193,209,225,241,255,257,289,321,353,385,417,449,481,511,513,545,
%U A338129 577,609,641,673,705,737,769,801,833,865,897,929,961,993,1023,1025
%N A338129 Positive numbers k such that the binary representation of k^k ends with that of k.
%C A338129 This sequence is infinite as it contains the positive terms of A000225.
%C A338129 All terms are odd.
%C A338129 Run lengths in first differences appear to be regular and suggest a simple procedure to generate the sequence.
%H A338129 Rémy Sigrist, <a href="/A338129/b338129.txt">Table of n, a(n) for n = 1..10000</a>
%H A338129 Rémy Sigrist, <a href="/A338129/a338129.png">Binary plot of the terms < 2^16</a>
%H A338129 <a href="/index/Ar#automorphic">Index entries for sequences related to automorphic numbers</a>
%e A338129 The binary representation of 3^3 ("11011") ends with that of 3 ("11"), so 3 is a term.
%t A338129 Select[Range[1200],Take[IntegerDigits[#^#,2],-IntegerLength[ #,2]] == IntegerDigits[ #,2]&] (* _Harvey P. Dale_, Jan 12 2022 *)
%o A338129 (PARI) is(n, base=2) = Mod(n, base^#digits(n, base))^n==n
%Y A338129 Cf. A000225, A082576, A338128, A338130.
%K A338129 nonn,base
%O A338129 1,2
%A A338129 _Rémy Sigrist_, Oct 11 2020