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A333447 a(n) is the integer corresponding to a bit-string representation of the von Neumann ordinal representation of n, with largest sets listed first, and with '{' represented by the bit 1, '}' represented by the bit zero, and ignoring commas. 1
2, 12, 228, 62052, 4180832868, 18201642257939067492, 338021701687178649306251838479209230948, 115407456979036362321626052309736660160730393295399201179594209600531491615332 (list; graph; refs; listen; history; text; internal format)



Since the von Neumann ordinals begin with 0={}, it seems appropriate to have an offset of 0.

The sequence grows super-exponentially.

Similar to A092124, except that A092124 reverses the order of the elements in the ordinal.

The binary expansion of a(n-1) has length 2^n and consists of n 1's followed by the leading terms of A308187. - Andrey Zabolotskiy, Mar 21 2020


Kit Scriven, Table of n, a(n) for n = 0..10

Johann von Neumann, Zur Einf├╝hrung der transfiniten Zahlen, Acta Litterarum AC Scientiarum Ragiae Universitatis Hungaricae Francisco-Josephinae, 1 (1923), 199-208.


a(0) = 2, a(n) = 2^(2^(n+1)-1) - 2^(2^(n)-1) + a(n-1)*(2^(2^(n)-1) + 1).


A table demonstrating the von Neumann ordinals of the first three integers, their corresponding bit strings, and their sequence values is as follows:

  n   set notation       bit string         a(n)

  0   {}                 10                 2

  1   {{}}               1100               12

  2   {{{}}{}}           11100100           228

  3   {{{{}}{}}{{}}{}}   1111001001100100   62052



def fBinDigit(n):

    return 2**(2**(n+1) - 1)

def a333447(n):

    if n==0:

        return 2


        prevAsEle = a333447(n-1) * fBinDigit(n-1)

        restOfEle = a333447(n-1) - fBinDigit(n-1)

        return fBinDigit(n)+prevAsEle+restOfEle


Cf. A079559, A092124, A308187.

Sequence in context: A132879 A101712 A156484 * A009272 A013141 A013143

Adjacent sequences:  A333444 A333445 A333446 * A333448 A333449 A333450




Kit Scriven, Mar 21 2020



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Last modified November 29 02:45 EST 2020. Contains 338756 sequences. (Running on oeis4.)