A137162 -id:A137162 - cp's OEIS frontend

A137161 Starting at Step=0 from the sequence 1, 0, 1, 0, 1, 0, etc. (A059841) at any Step=n, with n>=1, any numbers of the previous step is inserted in the sequence any (2*n-1) numbers.

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

Offset: 0

Paolo P. Lava and Giorgio Balzarotti, Jan 25 2008, Mar 05 2008

If the sequence is regarded as the binary representation of the number 0.1101011111110...... in decimal it is 0.843596927232253....

			Step n=0: 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, etc.
Step n=1: 2*n-1=1 thus after any 1 number -> 1 number of Step=0 is inserted
1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, etc.
Step n=2: 2*n-1=3 thus after any 3 numbers -> 1 number of Step=1 is inserted
1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, etc.
Step n=3: 2*n-1=5 thus after any 5 numbers -> 1 number of Step=2 is inserted
1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, etc.
And so on.

Cf. A137162, A137163.

A137163 Like sequence A137161 but starting from the sequence of natural number A000027.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 4, 1, 4, 1, 1, 1, 5, 1, 2, 1, 1, 1, 5, 1, 6, 1, 1, 1, 6, 1, 2, 1, 1, 1, 2, 1, 7, 1, 1, 1, 7, 1, 2, 1, 1, 1, 8, 1, 3, 1, 1

Offset: 0

Paolo P. Lava, Jan 28 2008

			Step=0 -> 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,..
Now any "1" position insert the numbers of Step=0.
Step=1 -> 1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,..
Now any "3" positions insert the numbers of Step=1
Step=2 -> 1,1,2,1,2,3,3,1,4,4,5,2,5,6,6,2,7,7,8,3,8,9,9,3,10,..
Now any "5" positions insert the numbers of Step=2
Step=3 -> 1,1,2,1,2,1,3,3,1,4,4,1,5,2,5,6,6,2,2,7,7,8,3,1,8,9,..
And so on.

Cf. A137161, A137162.

cp's OEIS Frontend

A137161 Starting at Step=0 from the sequence 1, 0, 1, 0, 1, 0, etc. (A059841) at any Step=n, with n>=1, any numbers of the previous step is inserted in the sequence any (2*n-1) numbers.

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