A275661 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.

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, 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, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0

Offset

1

Comments

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

Links

Table of n, a(n) for n=1..88.

Example

First step: 1; the two numbers are obviously 1 and 1 which sum to 10; sequence becomes 1,1,0;
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;
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.

Maple

with(numtheory): P:=proc(q) local a, b, c, d, k, n;  a:=[1];
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)];
for k from nops(a)-1 by -1 to 1 do c:=2*c+a[k]; od; d:=convert(b+c, binary);
for k from 1 to ilog10(d)+1 do a:=[op(a), (trunc(d/10^(ilog10(d)+1-k)) mod 10)] ; od;
od; print(a); end: P(10);

Mathematica

Nest[Join[#, IntegerDigits[FromDigits[#, 2] + FromDigits[Reverse@ #, 2], 2]] &, {1}, 6] (* Michael De Vlieger, Sep 02 2016 *)

Crossrefs

Cf. A269362.

Sequence in context: A176890 A164057 A140820 * A266716 A190242 A167501

Adjacent sequences: A275658 A275659 A275660 * A275662 A275663 A275664

Keyword

nonn,easy,base

Author

Paolo P. Lava, Sep 02 2016

Status

approved