login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A211344 Atomic Boolean functions interpreted as binary numbers. 2
1, 3, 5, 15, 51, 85, 255, 3855, 13107, 21845, 65535, 16711935, 252645135, 858993459, 1431655765, 4294967295, 281470681808895, 71777214294589695, 1085102592571150095, 3689348814741910323, 6148914691236517205 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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...

LINKS

Tilman Piesk, Table of n, a(n) for n = 0..65

Tilman Piesk, Atomic Boolean functions in Sierpinski triangle (Wikimedia Commons)

FORMULA

a = A001317( A089633 )

PROG

(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

CROSSREFS

A001317, A089633, A051179 (left diagonal)

Sequence in context: A103043 A018601 A190733 * A006394 A018650 A177814

Adjacent sequences:  A211341 A211342 A211343 * A211345 A211346 A211347

KEYWORD

nonn,tabl

AUTHOR

Tilman Piesk, Jul 24 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 8 01:14 EST 2016. Contains 278902 sequences.