A268034 A268032 with repeated 1's removed.

3, 5, 11, 3, 21, 3, 5, 43, 3, 5, 11, 3, 85, 3, 5, 11, 3, 21, 3, 5, 171, 3, 5, 11, 3, 21, 3, 5, 43, 3, 5, 11, 3, 341, 3, 5, 11, 3, 21, 3, 5, 43, 3, 5, 11, 3, 85, 3, 5, 11, 3, 21, 3, 5, 683, 3, 5, 11, 3, 21, 3, 5, 43, 3, 5

Offset: 1

Author

Jeremy Gardiner, Jan 24 2016

Keywords

• nonn

Comments

Records appear to be given by A001045 Jacobsthal numbers.

(a(n)-1)/2 appears to be A085358.

The terms between the A001045(n+3) are:

3

5

11

3,

21

3, 5,

43

3, 5, 11, 3,

85

3, 5, 11, 3, 21, 3, 5,

171

3, 5, 11, 3, 21, 3, 5, 43, 3, 5, 11, 3,

341

3, 5, 11, 3, 21, 3, 5, 43, 3, 5, 11, 3, 85, 3, 5, 11, 3, 21, 3, 5,

683

This gives the same sequence. Every column has the same number.

By rows, there are 0, 0, 1, 2, 4, 7, 12, 20, ... apparently = Fibonacci(n+1) - 1 = A000071 terms.

From Paul Curtz, Jan 26 2016: (Start)

a(n) is also in

0, 1, 1 0, 3, 0, 1, 5, 0, ... equivalent to A035614(n)

1, 1, 3, 1, 5, 1, 1, 11, 1, ... equivalent to A035612(n)

1, 3, 5, 1, 11, 1, 3, 21, 1, ... (compare to A268032)

3, 5, 11, 3, 21, 3, 5, 43, 3, ... a(n) (equivalent to a3(n) in A035612)

5, 11, 21, 5, 43, 5, 11, 85, 5, ...

etc.

Every vertical comes from A001045 (*).

Second row: first one removing all 0's.

Third row: second one removing a part of 1's respecting (*)

Fourth row: third one removing all 1's.

etc.

The offset 0 is homogeneous to these sequences. (End)

Examples

			A268032 begins 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 3, 1, 1, 1, 21, ... hence this sequence begins 3, 5, 11, 3, 21, ...
		

Crossrefs

Cf. A000071, A001045, A035612, A035614, A085358, A268032.