A347519 Square array read by antidiagonals upwards taken the terms of A347270 and replacing the powers of 2 with zeros and the nonpowers of 2 with ones, n >= 1, k >= 0.

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

Offset

1

Comments

The square array A347270 gives all 3x+1 sequences.

If n is a power of 2 then row n is A000004.

Links

Table of n, a(n) for n=1..99.

Index entries for sequences related to 3x+1 (or Collatz) problem

Example

The corner of the square array T(n,k) begins:
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
   1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
   1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
   1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
   1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
   1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, ...
   1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
   1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
   1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
   1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
   1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, ...
...
For n = 6 the 3x+1 sequence starting at 6 is 6, 3, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, ... The first four terms are nonpowers of 2. The fifth term and beyond are powers of 2. So row 6 is 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...

Crossrefs

Row sums give A208981.

Column 0 gives A043545.

Cf. A000004, A000079, A006370, A006577, A057716, A347270, A347283, A347523.

Sequence in context: A268310 A283316 A284508 * A160351 A268340 A355453

Adjacent sequences: A347516 A347517 A347518 * A347520 A347521 A347522

Keyword

nonn,tabl

Author

Omar E. Pol, Sep 04 2021

Status

approved