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.
For n=42: - the binary representation of 42 is "101010", - there are 7 ways to split it: - "" and "101010": x=0 and y=42: 0 XOR 42 = 42, - "1" and "01010": x=1 and y=10: 1 XOR 10 = 11, - "10" and "1010": x=2 and y=10: 2 XOR 10 = 8, - "101" and "010": x=5 and y=2: 5 XOR 2 = 7, - "1010" and "10": x=10 and y=2: 10 XOR 2 = 8, - "10101" and "0": x=21 and y=0: 21 XOR 0 = 21, - "101010" and "": x=42 and y=0: 42 XOR 0 = 42, - hence a(42) = 7.
a(n) = my (v=oo, b=binary(n)); for (w=0, #b, v=min(v, bitxor(fromdigits(b[1..w],2), fromdigits(b[w+1..#b],2)))); v
For n=42: - the binary representation of 42 is "101010", - there are 7 ways to split it: - "" and "101010": x=0 and y=42: abs(0 - 42) = 42, - "1" and "01010": x=1 and y=10: abs(1 - 10) = 9, - "10" and "1010": x=2 and y=10: abs(2 - 10) = 8, - "101" and "010": x=5 and y=2: abs(5 - 2) = 3, - "1010" and "10": x=10 and y=2: abs(10 - 2) = 8, - "10101" and "0": x=21 and y=0: abs(21 - 0) = 21, - "101010" and "": x=42 and y=0: abs(42 - 0) = 42, - hence a(42) = 3.
a(n) = my (v=oo, b=binary(n)); for (w=0, #b, v=min(v, abs(fromdigits(b[1..w],2) - fromdigits(b[w+1..#b],2)))); v
For n=42: - the binary representation of 42 is "101010", - there are 7 ways to split it: - "" and "101010": x=0 and y=42: abs(0^2 - 42^2) = 1764, - "1" and "01010": x=1 and y=10: abs(1^2 - 10^2) = 99, - "10" and "1010": x=2 and y=10: abs(2^2 - 10^2) = 96, - "101" and "010": x=5 and y=2: abs(5^2 - 2^2) = 21, - "1010" and "10": x=10 and y=2: abs(10^2 - 2^2) = 96, - "10101" and "0": x=21 and y=0: abs(21^2 - 0^2) = 441, - "101010" and "": x=42 and y=0: abs(42^2 - 0^2) = 1764, - hence a(42) = 21.
a(n) = my (v=oo, b=binary(n)); for (w=0, #b, v=min(v, abs(fromdigits(b[1..w],2)^2 - fromdigits(b[w+1..#b],2)^2))); v