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 A380544 #23 Jul 03 2025 17:39:03
%S A380544 0,3,5,9,15,17,27,33,51,63,65,99,119,129,195,231,255,257,387,455,495,
%T A380544 513,771,903,975,1023,1025,1539,1799,1935,2015,2049,3075,3591,3855,
%U A380544 3999,4095,4097,6147,7175,7695,7967,8127,8193,12291,14343,15375,15903,16191,16383,16385
%N A380544 Numbers of the form A073138(k) XOR A038573(k).
%C A380544 The plot of the sequence has a blancmange appearance. The discontinuities in the curve are at a(n) = k^2 + 1.
%C A380544 The bit length of a(n+1) appears to be A000267(n)+1.
%C A380544 The number of 0-bits in the binary expansion of a(n+1) appears to be A082375(n).
%e A380544 k = 17. A073138(17) = 24 = 11000_2. A038573(17) = 3 = 00011_2. 11000_2 XOR 00011_2 = 11011_2 = 27. 27 is a term.
%t A380544 s[n_, k_] := (2^n-1)*(2^(k-n)+1); Join[{0}, Table[s[n, k], {k, 2, 15}, {n, 1, Floor[k/2]}] // Flatten] (* _Amiram Eldar_, Jun 23 2025 *)
%o A380544 (PARI) a8(n) = fromdigits(vecsort(binary(n), , 4), 2);
%o A380544 a3(n) = 2^hammingweight(n)-1;
%o A380544 lista(nn) = Set(vector(nn, n, bitxor(a3(n), a8(n)))); \\ _Michel Marcus_, Jun 23 2025
%Y A380544 Cf. A073138, A038573, A000267, A082375.
%Y A380544 Subsequence of A006995.
%K A380544 base,easy,nonn,look
%O A380544 1,2
%A A380544 _Frederik P.J. Vandecasteele_, Jun 23 2025
%E A380544 More terms from _Michel Marcus_, Jun 23 2025