A380544 Numbers of the form A073138(k) XOR A038573(k).

0, 3, 5, 9, 15, 17, 27, 33, 51, 63, 65, 99, 119, 129, 195, 231, 255, 257, 387, 455, 495, 513, 771, 903, 975, 1023, 1025, 1539, 1799, 1935, 2015, 2049, 3075, 3591, 3855, 3999, 4095, 4097, 6147, 7175, 7695, 7967, 8127, 8193, 12291, 14343, 15375, 15903, 16191, 16383, 16385

Offset: 1

Author

Frederik P.J. Vandecasteele, Jun 23 2025

Keywords

• base
• easy
• nonn
• look

Comments

The plot of the sequence has a blancmange appearance. The discontinuities in the curve are at a(n) = k^2 + 1.

The bit length of a(n+1) appears to be A000267(n)+1.

The number of 0-bits in the binary expansion of a(n+1) appears to be A082375(n).

Examples

			k = 17. A073138(17) = 24 = 11000_2. A038573(17) = 3 = 00011_2. 11000_2 XOR 00011_2 = 11011_2 = 27. 27 is a term.
		

Crossrefs

Cf. A073138, A038573, A000267, A082375.

Subsequence of A006995.

Programs

Mathematica

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 *)

PARI

a8(n) = fromdigits(vecsort(binary(n), , 4), 2);
a3(n) = 2^hammingweight(n)-1;
lista(nn) = Set(vector(nn, n, bitxor(a3(n), a8(n)))); \\ Michel Marcus, Jun 23 2025

Extensions

More terms from Michel Marcus, Jun 23 2025