A122244 -id:A122244 - cp's OEIS frontend

A122245 a(n) = A014486(A122244(n)).

44, 232, 920, 3876, 14936, 60568, 248240, 996440, 3876264, 15524272, 63773584, 255477160, 993549616, 3970767760, 16350559552, 65386339632, 254129067336, 1016476056896, 4184726043136, 16740063237448, 65054466609736, 260416091191808

Offset: 1

Antti Karttunen, Sep 14 2006

Questions: to which Wolfram's class does this simple program belong, class 3 or class 4? (Is that classification applicable here? This is not 1D CA, although it may look like one).
Does the "central skyscraper" continue widening forever? (see the image for up to 16384th generation) At what specific points it widens? (A new sequence for that). How does that differ from A122242 and similar sister sequences, with different starting conditions?
Related comments in A179777.

Antti Karttunen, Table of n, a(n) for n = 1..1024
A. Karttunen, Python program for computing this sequence and the associated image.
A. Karttunen, Terms a(1)-a(768) drawn as binary strings, in Wolframesque fashion.
A. Karttunen, Terms a(1)-a(256) drawn as binary strings, showing details better.
Antti Karttunen, The central parts of terms a(1) - a(16384) drawn in similar fashion, showing how the "crystallized central skyscraper" gets slowly wider and wider

A122246 shows the same sequence in binary. Compare to similar Wolframesque plots given in A080070, A122229, A122232, A122235, A122239, A122242, A179755, A179757. Cf. also A179777, A179762, A179417.

A179846 a(n) = A179752(A122244(n)).

Original entry on oeis.org

2, 3, 3, 4, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 5, 4, 6, 9, 5, 7, 9, 8, 7, 5, 8, 6, 7, 7, 8, 7, 7, 8, 11, 7, 10, 11, 10, 10, 12, 10, 10, 12, 11, 10, 11, 11, 10, 11, 8, 10, 11, 11, 11, 12, 12, 11, 12, 12, 12, 11, 14, 12, 11, 14, 13, 11, 11, 13, 13, 15, 14, 13, 17, 14, 16, 17, 13, 16, 14

Offset: 1

Antti Karttunen, Aug 03 2010

nonn

a(n) is also the local maximum of A179765 in range [(2*A000217(n+1))-5,(2*A000217(n+2))-6].

A. Karttunen, Table of n, a(n) for n = 1..1024

Cf. also A179842 & A179844-A179847.

A179842 a(n) = A179751(A122244(n)).

Original entry on oeis.org

3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 7, 9, 10, 9, 10, 11, 12, 10, 11, 12, 12, 10, 11, 12, 10, 11, 11, 14, 14, 12, 15, 16, 14, 15, 16, 17, 15, 16, 17, 18, 17, 19, 18, 17, 19, 16, 16, 17, 17, 17, 18, 19, 21, 21, 19, 21, 21, 21, 20, 19, 21, 20, 19, 18, 19, 17, 19, 28, 29, 27, 30, 32

Offset: 1

Antti Karttunen, Aug 03 2010

nonn

A. Karttunen, Table of n, a(n) for n = 1..1024

Cf. also A179846 & A179840-A179843.

A122237 a(n) = A057548(A082358(n)).

Original entry on oeis.org

1, 3, 8, 7, 22, 21, 18, 17, 20, 64, 63, 59, 58, 62, 50, 49, 46, 45, 48, 61, 57, 55, 54, 196, 195, 190, 189, 194, 176, 175, 171, 170, 174, 193, 188, 185, 184, 148, 147, 143, 142, 146, 134, 133, 130, 129, 132, 145, 141, 139, 138, 192, 187, 173, 169, 183, 181, 167

Offset: 0

Antti Karttunen, Sep 14 2006

nonn

Iterates: A106191, A122241, A122244. Cf. also A122227, A080067.

A376405 Bitwise XOR (centrally aligned) of two consecutive terms of A122245.

Original entry on oeis.org

176, 584, 2068, 9232, 38952, 135296, 567096, 2444568, 10136288, 34920688, 144732808, 625792608, 2598216176, 8989149792, 37119010736, 160422522664, 665656629200, 2297815400576, 9505629937992, 41066855413976, 169932530966160, 589165636912400, 2439104800321640, 10514745879265952, 43543845360254320, 149771860125187648

Offset: 1

Antti Karttunen, Sep 22 2024

Antti Karttunen, Table of n, a(n) for n = 1..1650
Antti Karttunen, Python program for computing this sequence and the associated images.
Antti Karttunen, Terms a(1)-a(2048) drawn as binary strings, in Wolframesque fashion.
Index entries for sequences related to binary expansion of n

Cf. A122245 (A014486, A057548, A082358, A122237, A122244).

Cf. also A327973, A376402, A376415.

A376405(n) = bitxor(A122245(1+n), 2*A122245(n));

Python
```
# See the Links section
```

a(n) = A122245(1+n) XOR 2*A122245(n).

A376415 a(n) = A122245(4+n) XOR 16*A122245(n).

Original entry on oeis.org

14488, 57880, 258096, 1033752, 3702824, 14821424, 66158736, 264831016, 948570032, 3798139024, 16949183552, 67829237680, 243080889928, 972279514176, 4341071097344, 17360471721544, 62225889019592, 248568875068928, 1111070190653712, 4438793067349704, 15908408008868528, 63634253845942544, 284082756299099488, 1136310075423425200

Offset: 1

Antti Karttunen, Sep 22 2024

This seems to preserve more of the "wavy texture" present in A122245 than what A376412 does vis-a-vis A122242. Compare the corresponding illustrations.

Antti Karttunen, Table of n, a(n) for n = 1..1650
Antti Karttunen, Python program for computing this sequence and the associated images.
Antti Karttunen, Terms a(1)-a(768) drawn as binary strings, in Wolframesque fashion.
Antti Karttunen, The central parts of terms a(1) - a(20000) drawn in similar fashion. (the widening blank region in the middle corresponds with the "central crystallization" attractor present in A122245)
Index entries for sequences related to binary expansion of n

Cf. A122245 (A014486, A057548, A082358, A122237, A122244).

Cf. also A327973, A376405, A376412.

A376415(n) = bitxor(A122245(4+n), 16*A122245(n));

Python
```
# See the Links section
```

cp's OEIS Frontend

A122245 a(n) = A014486(A122244(n)).

Views

Author

Keywords

Comments

Links

Crossrefs

A179846 a(n) = A179752(A122244(n)).

Views

Author

Keywords

Comments

Links

Crossrefs

A179842 a(n) = A179751(A122244(n)).

Views

Author

Keywords

Links

Crossrefs

A122237 a(n) = A057548(A082358(n)).

Views

Author

Keywords

Crossrefs

A376405 Bitwise XOR (centrally aligned) of two consecutive terms of A122245.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Python

Formula

A376415 a(n) = A122245(4+n) XOR 16*A122245(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Python