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A333447
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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.
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3
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2, 12, 228, 62052, 4180832868, 18201642257939067492, 338021701687178649306251838479209230948, 115407456979036362321626052309736660160730393295399201179594209600531491615332
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OFFSET
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0,1
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COMMENTS
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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
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LINKS
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FORMULA
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a(0) = 2, a(n) = 2^(2^(n+1)-1) - 2^(2^(n)-1) + a(n-1)*(2^(2^(n)-1) + 1).
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EXAMPLE
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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
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MATHEMATICA
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With[{nmax=8}, Map[FromDigits[#, 2]&, NestList["1"<>#<>StringTake[#, {2, -2}]<>"0"&, "10", nmax]]] (* Paolo Xausa, Nov 21 2023 *)
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PROG
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(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
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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