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A227723 Smallest Boolean functions from big equivalence classes (counted by A000616). 5
0, 1, 3, 6, 7, 15, 22, 23, 24, 25, 27, 30, 31, 60, 61, 63, 105, 107, 111, 126, 127, 255, 278, 279, 280, 281, 282, 283, 286, 287, 300, 301, 303, 316, 317, 318, 319, 360, 361, 362, 363, 366, 367, 382, 383, 384, 385, 386, 387, 390, 391, 393, 395 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Two Boolean functions belong to the same big equivalence class (bec) when they can be expressed by each other by negating and permuting arguments. E.g., when f(~p,r,q) = g(p,q,r), then f and g belong to the same bec. Geometrically this means that the functions correspond to hypercubes with binarily colored vertices that are equivalent up to rotation and reflection.
Boolean functions correspond to integers, so each bec can be denoted by the smallest integer corresponding to one of its functions. There are A000616(n) big equivalence classes of n-ary Boolean functions. Ordered by size they form the finite sequence A_n. It is the beginning of A_(n+1), which leads to this infinite sequence A.
LINKS
Tilman Piesk, bec of 4-ary functions corresponding to a(85) = 854 = 0x0356
FORMULA
a( A000616 - 1 ) = a(2,5,21,401,...) = 3,15,255,65535,... = A051179
EXAMPLE
The 16 2-ary functions ordered in A000616(2) = 6 big equivalence classes:
a a(n) Boolean functions hypercube (square)
0 0 0000 empty
1 1 0001, 0010, 0100, 1000 one in a corner
2 3 0011, 1100, 0101, 1010 ones on a side
3 6 0110, 1001 ones on a diagonal
4 7 0111, 1011, 1101, 1110 ones in 3 corners
5 15 1111 full
CROSSREFS
Cf. A227722 (does the same for small equivalence classes).
Sequence in context: A281900 A266615 A043305 * A192124 A334210 A072773
KEYWORD
nonn
AUTHOR
Tilman Piesk, Jul 22 2013
STATUS
approved

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Last modified July 20 14:50 EDT 2024. Contains 374459 sequences. (Running on oeis4.)