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A211344
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Atomic Boolean functions interpreted as binary numbers.
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1
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1, 3, 5, 15, 51, 85, 255, 3855, 13107, 21845, 65535, 16711935, 252645135, 858993459, 1431655765, 4294967295, 281470681808895, 71777214294589695, 1085102592571150095, 3689348814741910323, 6148914691236517205
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OFFSET
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0,2
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COMMENTS
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Row n of the triangle shows the atoms among n-ary Boolean functions:
1 01
3 5 0011 0101
15 51 85 00001111 00110011 01010101
Often n-ary x_k = T(n,k), e.g. for 2-ary functions x_1=0011, x_2=0101 and for 3-ary functions x_1=00001111, x_2=00110011, x_3=01010101.
An easier generalized way is the enumeration from right to left (preferably from x_0) so that n-ary x_k = T(n,n-k). As numbers in the diagonals on the right have the same bit pattern this goes well together with the infinitary definition of atomic formulas as x_k = 1/A000215(k) = 1/(2^2^k+1) in binary:
2-ary x_0=0101=5, 3-ary x_0=01010101=85, infinitary x_0=1/3=.010101...
2-ary x_1=0011=3, 3-ary x_1=00110011=51, infinitary x_1=1/5=.001100110011...
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LINKS
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Tilman Piesk, Table of n, a(n) for n = 0..65
Tilman Piesk, Atomic Boolean functions in Sierpinski triangle (Wikimedia Commons)
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FORMULA
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a = A001317( A089633 )
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PROG
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(Matlab)
Seq = sym(zeros(55, 1)) ;
Filledlines = 0 ;
for m=1:10
for n=1:m
Sum = sym(0) ;
for k=0:2^m-1
if mod( floor( k/2^(m-n) ) , 2) == 0
Sum = Sum + 2^sym(k) ;
end
end
Seq( Filledlines + n ) = Sum ;
end
Filledlines = Filledlines + m ;
end
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CROSSREFS
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A001317, A089633, A051179 (left diagonal)
Sequence in context: A103043 A018601 A190733 * A006394 A018650 A177814
Adjacent sequences: A211341 A211342 A211343 * A211346 A211347 A211348
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KEYWORD
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nonn,tabl
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AUTHOR
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Tilman Piesk, Jul 24 2012
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STATUS
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approved
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