A376412 -id:A376412 - cp's OEIS frontend

A122242 a(n) = A014486(A122241(n)).

42, 240, 916, 3748, 14960, 62104, 248176, 969304, 3876576, 15962544, 63772488, 248169896, 993554240, 4086635408, 16350541128, 63529835824, 254129143040, 1046249323840, 4184725760584, 16276030608712, 65054467548432, 267635134298624

Offset: 1

Antti Karttunen, Sep 14 2006

Question: to which Wolfram's class does this simple program belong, class 3 or class 4, or is such categorization at all applicable here?

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, Terms a(1)-a(256) drawn as binary strings, showing details better.
Antti Karttunen, The central parts of terms a(1) - a(20000) drawn in similar fashion. (Note the "foreshadowing ghost columns" present in the "central skyscraper" attractor that are not present at A122245. Compare also to illustrations in A376412)
Index entries for sequences related to binary expansion of n
Index entries for encodings of plane rooted trees
Index entries for sequences related to parenthesizing

Cf. A014486, A057548, A082358, A122237, A122241, A122243 (same sequence in binary).
Compare to similar Wolframesque plots given in A080070, A122229, A122232, A122235, A122239, A122245.
Cf. also A376402, A376412.

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

For n >= 1, a(1+n) = 2*a(n) XOR A376402(n), a(4+n) = 16*a(n) XOR A376412(n). - Antti Karttunen, Sep 23 2024

A376402 Bitwise XOR (centrally aligned) of two consecutive terms of A122242.

Original entry on oeis.org

164, 628, 2444, 10040, 34424, 142400, 612536, 2536016, 8772720, 36320296, 156298040, 648930320, 2246427920, 9290072680, 40123676576, 166398412640, 574717970240, 2376856817864, 10244120543704, 42544644116352, 146496800436256, 607708669110320, 2625008220416552, 10882360875506928, 37586414897168848, 156056124134144296

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. A122242 (A014486, A057548, A082358, A122237, A122241).

Cf. also A327973, A376405, A376412.

A376402(n) = bitxor(A122242(1+n), 2*A122242(n));

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

a(n) = A122242(1+n) XOR 2*A122242(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

A122242 a(n) = A014486(A122241(n)).

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A376402 Bitwise XOR (centrally aligned) of two consecutive terms of A122242.

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Author

Keywords

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Programs

PARI

Python

Formula

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

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Author

Keywords

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Crossrefs

Programs

PARI

Python