login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)
OFFSET

0,1

COMMENTS

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

LINKS

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.

FORMULA

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

EXAMPLE

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

PROG

(Python)

def fBinDigit(n):

    return 2**(2**(n+1) - 1)

def a333447(n):

    if n==0:

        return 2

    else:

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

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

        return fBinDigit(n)+prevAsEle+restOfEle

CROSSREFS

Cf. A079559, A092124, A308187.

Sequence in context: A132879 A101712 A156484 * A009272 A013141 A013143

Adjacent sequences:  A333444 A333445 A333446 * A333448 A333449 A333450

KEYWORD

nonn

AUTHOR

Kit Scriven, Mar 21 2020

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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