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A308705
Decimal expansion of the constant formed by concatenating the terms of A076478 (binary vectors of lengths 1, 2, 3, ... in numerical order).
0
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
OFFSET
0,1
COMMENTS
The binary vectors "0,1,00,01,10,11,000,001,..." are concatenated into a constant "0.0100011011000001...", then converted to decimal.
EXAMPLE
0.276387117279486523734198676211901230555089988160685506143676819115...
MATHEMATICA
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 *)
PROG
(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:]))
CROSSREFS
Cf. A076478.
Sequence in context: A334366 A350761 A135155 * A244847 A175477 A333521
KEYWORD
nonn,base,cons
AUTHOR
David McFadzean, Jun 18 2019
STATUS
approved