Kit Scriven - cp's OEIS frontend

User: Kit Scriven

Kit Scriven has authored 2 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.

2, 12, 228, 62052, 4180832868, 18201642257939067492, 338021701687178649306251838479209230948, 115407456979036362321626052309736660160730393295399201179594209600531491615332

Offset: 0

Kit Scriven, Mar 21 2020

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

			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

Kit Scriven, Table of n, a(n) for n = 0..10
Johann von Neumann, Zur Einführung der transfiniten Zahlen, Acta Litterarum AC Scientiarum Ragiae Universitatis Hungaricae Francisco-Josephinae, 1 (1923), 199-208.

Cf. A079559, A092124, A308187.

With[{nmax=8},Map[FromDigits[#,2]&,NestList["1"<>#<>StringTake[#,{2,-2}]<>"0"&,"10",nmax]]] (* Paolo Xausa, Nov 21 2023 *)

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

from functools import lru_cache
@lru_cache(maxsize=None)
def A333447(n): return (1<<((m:=1<A333447(n-1) if n else 2 # Chai Wah Wu, Nov 23 2023

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

A255873 The first nonzero digit of n/7.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Kit Scriven, Mar 08 2015

			The leading (most significant) digit of 22/7 in A068028 is 3, so a(22)=3.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A020806 (1/7), A068028 (22/7), A216606 (360/7).

A255873 := proc(n)
    local nshf ;
    nshf := n/7 ;
    while nshf < 1 do
        nshf := 10*nshf;
    end do;
    while nshf >= 10 do
        nshf := nshf/10;
    end do;
    floor(nshf) ;
end proc: # R. J. Mathar, May 28 2016

f[n_] := RealDigits[n/7, 10, 9][[1, 1]]; Array[f, 105] (* Robert G. Wilson v, Mar 08 2015 *)

a(n) = {my(x = n/7.0); if (x < 1, x *= 10); while (x >= 10, x /= 10); floor(x);} \\ Michel Marcus, Mar 12 2015

cp's OEIS Frontend

User: Kit Scriven

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.

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