Boolf prop/3-ary/badge

The red circles mark the values 0..7 for the 3-ary BF.
(The black dots correspond to the atomvals.)

This is the XOR of all binary exponents of the Zhegalkin index. The corresponding sequence is A261283 (or A253315 with redundant entries).
Compare consul, twin prefect.

Number of blocks:   8 Integer partition:   8⋅32

# twin consul block
32 0 [0, 1, 2, 3, 4, 5, 6, 7, 16, 17, 18, 19, 20, 21, 22, 23, 232, 233, 234, 235, 236, 237, 238, 239, 248, 249, 250, 251, 252, 253, 254, 255]
32 4 [8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31, 224, 225, 226, 227, 228, 229, 230, 231, 240, 241, 242, 243, 244, 245, 246, 247]
32 2 [32, 33, 34, 35, 36, 37, 38, 39, 48, 49, 50, 51, 52, 53, 54, 55, 200, 201, 202, 203, 204, 205, 206, 207, 216, 217, 218, 219, 220, 221, 222, 223]
32 6 [40, 41, 42, 43, 44, 45, 46, 47, 56, 57, 58, 59, 60, 61, 62, 63, 192, 193, 194, 195, 196, 197, 198, 199, 208, 209, 210, 211, 212, 213, 214, 215]
32 1 [64, 65, 66, 67, 68, 69, 70, 71, 80, 81, 82, 83, 84, 85, 86, 87, 168, 169, 170, 171, 172, 173, 174, 175, 184, 185, 186, 187, 188, 189, 190, 191]
32 5 [72, 73, 74, 75, 76, 77, 78, 79, 88, 89, 90, 91, 92, 93, 94, 95, 160, 161, 162, 163, 164, 165, 166, 167, 176, 177, 178, 179, 180, 181, 182, 183]
32 3 [96, 97, 98, 99, 100, 101, 102, 103, 112, 113, 114, 115, 116, 117, 118, 119, 136, 137, 138, 139, 140, 141, 142, 143, 152, 153, 154, 155, 156, 157, 158, 159]
32 7 [104, 105, 106, 107, 108, 109, 110, 111, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 144, 145, 146, 147, 148, 149, 150, 151]
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