cp's OEIS Frontend

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

%I A348162 #25 Nov 20 2021 20:41:54
%S A348162 0,0,2,38,9782,641083190,2753431335706502966,
%T A348162 50791843174310108512166439539235563318,
%U A348162 17283568615631356151658578642396687258566665947274335391075779120894446085942
%N A348162 a(n) is the previous term in binary with 0's and 1's put alternatingly before each digit, starting with 0.
%C A348162 The next term is too large to include.
%C A348162 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.
%e A348162 a(2) = 0010;
%e A348162 a(3) = (0010 + 0101 -> 00100110);
%e A348162 a(4) = (00100110 + 01010101 = 0010011000110110).
%e A348162 Full explanation:
%e A348162 Say we have the term 0010.
%e A348162 We get an equal length binary number of alternating 0s and 1s.
%e A348162 In this case it would be 0101, and we interlace them like so:
%e A348162                 0   1   0   1
%e A348162 0010 + 0101 ->    0   0   1   0  -> 00100110
%o A348162 (Python)
%o A348162 def combine(a,b):
%o A348162   c = ''
%o A348162   for i in range(max(len(a),len(b))*2):
%o A348162    if i%2 == 0:
%o A348162     if len(a) > i/2:
%o A348162      c += (a[int(i/2)])
%o A348162    else:
%o A348162     if len(b) > i/2:
%o A348162      c += (b[int(i/2)])
%o A348162   return c
%o A348162 x = '0'
%o A348162 while True:
%o A348162   x = combine(combine(len(x)*'0',len(x)*'1')[:len(x)],x)
%o A348162 (Python)
%o A348162 from itertools import islice
%o A348162 def A348162(): # generator of terms
%o A348162     s = '0'
%o A348162     while True:
%o A348162         yield int(s,2)
%o A348162         s = ''.join(x+y for x, y in zip('01'*((len(s)+1)//2),s))
%o A348162 A348162_list = list(islice(A348162(),9)) # _Chai Wah Wu_, Nov 19 2021
%o A348162 (PARI) a(n) = my(ret=0,s=1); for(i=2,n, ret += 1<<s + ret<<(s<<=1)); ret; \\ _Kevin Ryde_, Nov 19 2021
%Y A348162 Cf. A014707 (bits of terms), A337580.
%K A348162 nonn,base
%O A348162 0,3
%A A348162 _Edward Green_, Oct 03 2021