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 A348162 a(n) is the previous term in binary with 0's and 1's put alternatingly before each digit, starting with 0. 2
 0, 0, 2, 38, 9782, 641083190, 2753431335706502966, 50791843174310108512166439539235563318, 17283568615631356151658578642396687258566665947274335391075779120894446085942 (list; graph; refs; listen; history; text; internal format)
 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 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<

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)