A348162 a(n) is the previous term in binary with 0's and 1's put alternatingly before each digit, starting with 0.

0, 0, 2, 38, 9782, 641083190, 2753431335706502966, 50791843174310108512166439539235563318, 17283568615631356151658578642396687258566665947274335391075779120894446085942

Offset: 0

Author

Edward Green, Oct 03 2021

Keywords

• nonn
• base

Comments

The next term is too large to include.

The actual sequence in binary is 0, 00, 0010, 00100110, ... The 0s at the start of each term are required for the sequence to work.

Examples

			a(2) = 0010;
a(3) = (0010 + 0101 -> 00100110);
a(4) = (00100110 + 01010101 = 0010011000110110).
Full explanation:
Say we have the term 0010.
We get an equal length binary number of alternating 0s and 1s.
In this case it would be 0101, and we interlace them like so:
                0   1   0   1
0010 + 0101 ->    0   0   1   0  -> 00100110
		

Crossrefs

Cf. A014707 (bits of terms), A337580.

Programs

PARI

a(n) = my(ret=0,s=1); for(i=2,n, ret += 1<Kevin Ryde, Nov 19 2021

Python

def combine(a,b):
  c = ''
  for i in range(max(len(a),len(b))*2):
   if i%2 == 0:
    if len(a) > i/2:
     c += (a[int(i/2)])
   else:
    if len(b) > i/2:
     c += (b[int(i/2)])
  return c
x = '0'
while True:
  x = combine(combine(len(x)*'0',len(x)*'1')[:len(x)],x)

Python

from itertools import islice
def A348162(): # generator of terms
    s = '0'
    while True:
        yield int(s,2)
        s = ''.join(x+y for x, y in zip('01'*((len(s)+1)//2),s))
A348162_list = list(islice(A348162(),9)) # Chai Wah Wu, Nov 19 2021