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

0,3

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.

Links

Table of n, a(n) for n=0..8.

Example

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

Prog

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

Crossrefs

Cf. A014707 (bits of terms), A337580.

Sequence in context: A288027 A184994 A334554 * A132396 A263374 A066244

Adjacent sequences: A348159 A348160 A348161 * A348163 A348164 A348165

Keyword

nonn,base

Author

Edward Green, Oct 03 2021

Status

approved