A308705 Decimal expansion of the constant formed by concatenating the terms of A076478 (binary vectors of lengths 1, 2, 3, ... in numerical order).

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

Author

David McFadzean, Jun 18 2019

Keywords

• nonn
• base
• cons

Comments

The binary vectors "0,1,00,01,10,11,000,001,..." are concatenated into a constant "0.0100011011000001...", then converted to decimal.

Examples

			0.276387117279486523734198676211901230555089988160685506143676819115...
		

Crossrefs

Cf. A076478.

Programs

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 *)

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:]))