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A308705
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Decimal expansion of the constant formed by concatenating the terms of A076478 (binary vectors of lengths 1, 2, 3, ... in numerical order).
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0
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2, 7, 6, 3, 8, 7, 1, 1, 7, 2, 7, 9, 4, 8, 6, 5, 2, 3, 7, 3, 4, 1, 9, 8, 6, 7, 6, 2, 1, 1, 9, 0, 1, 2, 3, 0, 5, 5, 5, 0, 8, 9, 9, 8, 8, 1, 6, 0, 6, 8, 5, 5, 0, 6, 1, 4, 3, 6, 7, 6, 8, 1, 9, 1, 1, 5
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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The binary vectors "0,1,00,01,10,11,000,001,..." are concatenated into a constant "0.0100011011000001...", then converted to decimal.
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LINKS
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EXAMPLE
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0.276387117279486523734198676211901230555089988160685506143676819115...
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MATHEMATICA
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m = 100; d[n_] := Rest@IntegerDigits[n + 1, 2] + 1; v = Flatten[Array[d, 4 m]] - 1; RealDigits[FromDigits[v, 2]/2^Length[v], 10, m][[1]] (* Amiram Eldar, Jul 05 2019 after Clark Kimberling at A076478 *)
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PROG
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(Python)
from bigfloat import *
import string
def GenerateBitstring(bitstring, suffix, recurse):
if recurse == 0:
bitstring = bitstring + suffix
else:
bitstring = GenerateBitstring(bitstring, suffix + "0", recurse-1)
bitstring = GenerateBitstring(bitstring, suffix + "1", recurse-1)
return bitstring
VulcanBinary = ""
MaxRecursion = 8
for i in range(1, MaxRecursion+1):
VulcanBinary = GenerateBitstring(VulcanBinary, "", i)
print('.' + VulcanBinary)
with precision(2000):
VulcanDecimal = BigFloat(0)
b = BigFloat(1)
for c in VulcanBinary:
b = b/2.
if c == '1':
VulcanDecimal = VulcanDecimal+b
print(VulcanDecimal)
print(string.join(x + ', ' for x in str(VulcanDecimal)[2:]))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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