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%I #19 Aug 25 2019 15:33:21
%S 1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,
%T 0,1,0,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,
%U 0,1,1,0,0,1,0,1,0,0,0,1,1,0,1,0,1,1,1,0
%N a(1)=1. At any step consider the stream of 0's and 1's as two base-2 numbers: the first reading from left to right and the second from right to left. Sum the two numbers in base 2 and add them to the end of the sequence. Repeat.
%C Decimal values of string of bits generated at the n-th step: {1, 6, 105, 27060, 1773437055, 7616854156643735370, 140506159274377790195414803346835746325, ...}. - _Michael De Vlieger_, Sep 02 2016
%e First step: 1; the two numbers are obviously 1 and 1 which sum to 10; sequence becomes 1,1,0;
%e Second step: 1,1,0; the two numbers are 110 and 11, which sum to 1001; sequence becomes 1,1,0,1,0,0,1;
%e Third step: 1,1,0,1,0,0,1; the two numbers are 1101001 and 1001011, which sum to 10110100; sequence becomes 1,1,0,1,0,0,1,1,0,1,1,0,1,0,0; etc.
%p with(numtheory): P:=proc(q) local a,b,c,d,k, n; a:=[1];
%p for n from 1 to q do b:=a[1]; for k from 2 to nops(a) do b:=2*b+a[k]; od; c:=a[nops(a)];
%p for k from nops(a)-1 by -1 to 1 do c:=2*c+a[k]; od; d:=convert(b+c,binary);
%p for k from 1 to ilog10(d)+1 do a:=[op(a),(trunc(d/10^(ilog10(d)+1-k)) mod 10)] ; od;
%p od; print(a); end: P(10);
%t Nest[Join[#, IntegerDigits[FromDigits[#, 2] + FromDigits[Reverse@ #, 2], 2]] &, {1}, 6] (* _Michael De Vlieger_, Sep 02 2016 *)
%Y Cf. A269362.
%K nonn,easy,base
%O 1
%A _Paolo P. Lava_, Sep 02 2016
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