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

0,1

Comments

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

Links

Table of n, a(n) for n=0..65.

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

Adjacent sequences: A308702 A308703 A308704 * A308706 A308707 A308708

Keyword

nonn,base,cons

Author

David McFadzean, Jun 18 2019

Status

approved