cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A218791 a(n) = binary code (shown here in decimal) of the position of the predecessor of the natural number pair (2n,2n+1) in the compact beanstalk-tree A218780.

Original entry on oeis.org

1, 2, 6, 10, 26, 58, 42, 74, 202, 458, 330, 842, 586, 1354, 1610, 2634, 6730, 14922, 10826, 27210, 19018, 43594, 51786, 117322, 84554, 182858, 215626, 313930, 477770, 838218, 576074, 1100362, 3197514, 7391818, 5294666, 13683274, 9488970, 22071882, 26266186
Offset: 1

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Author

Antti Karttunen, Nov 16 2012

Keywords

Links

Crossrefs

Subset of A218615, i.e., a(n) = A218615(A005187(n)).
Also, a(n) = A054429(A218790(n)). (Note also how the first five or so terms are twice the terms in the beginning of A218790, shifted by one term.)
Used to construct A218780, A218781. Cf. also A218787, A218788.

Formula

a(n) = A218615(A005187(n)).

A218776 A014486-codes for the Beanstalk-tree growing one natural number at time, starting from the tree of one internal node (1), with the "lesser numbers to the left hand side" construction.

Original entry on oeis.org

2, 12, 50, 204, 818, 3298, 13202, 52834, 211346, 845586, 3382418, 13531282, 54125714, 216503058, 866012306, 3464049426, 13856197778, 55424792722, 221699171474, 886796698770, 3547186799762, 14188747200658, 56754988803218, 227019955225746, 908079820907666
Offset: 1

Views

Author

Antti Karttunen, Nov 17 2012

Keywords

Comments

The active middle region of the triangle (see attached "Wolframesque" illustration) corresponds to the area where the growing tip(s) of the beanstalk are located. Successively larger "turbulences" occurring in that area appear approximately at the row numbers given by A218548. The larger tendrils (the finite side-trees) are, the longer there is vacillation in the direction of the growing region, which lasts until the growing tip of the infinite stem (A179016) has passed the topmost tips of the tendril. See also A218612.
These are the mirror-images (in binary tree sense) of the terms in sequence A218778. For more compact versions, see A218780 & A218782.

Examples

			Illustration how the growing beanstalk-tree produces the first four terms of this sequence. In this variant, the lesser numbers come to the left hand side:
..........
...\1/.... Coded by A014486(A218777(1)) = A014486(1) = 2 (binary 10).
..........
..........
.\2/......
...\1/.... Coded by A014486(A218777(2)) = A014486(3) = 12 (bin. 1100).
..........
..........
.\2/ \3/..
...\1/.... Coded by A014486(A218777(3)) = A014486(6) = 50 (110010).
..........
..........
....\4/...
.\2/.\3/..
...\1/.... Coded by A014486(A218777(4)) = A014486(15) = 204 (11001100).
..........
Thus the first four terms of this sequence are 2, 12, 50 and 204.

Links

Crossrefs

a(n) = A014486(A218777(n)). Cf. A014486, A218615, A218780, A218782, A218787, A218778.

A218778 A014486-codes for the Beanstalk-tree growing one natural number at time, starting from the tree of one internal node (1), with the "lesser numbers to the right side" construction.

Original entry on oeis.org

2, 10, 50, 210, 914, 3666, 14738, 59026, 236690, 946834, 3787922, 15151762, 60607634, 242437266, 969821330, 3879357586, 15518026898, 62072179858, 248289315986, 993157336210, 3972629941394, 15890526653586, 63562180611218, 254248729332882, 1016994991328402
Offset: 1

Views

Author

Antti Karttunen, Nov 17 2012

Keywords

Comments

The active middle region of the triangle (see attached "Wolframesque" illustration) corresponds to the area where the growing tip(s) of the beanstalk are located. Successively larger "turbulences" occurring in that area appear approximately at the row numbers given by A218548. The larger tendrils (the finite side-trees) are, the longer there is vacillation in the direction of the growing region, which lasts until the growing tip of the infinite stem (A179016) has passed the topmost tips of the tendril. See also A218612.
These are the mirror-images (in binary tree sense) of the terms in sequence A218776. For more compact versions, see A218780 & A218782.

Examples

			Illustration how the growing beanstalk-tree produces the first four terms of this sequence. In this variant, the lesser numbers come to the right hand side:
..........
...\1/.... Coded by A014486(A218779(1)) = A014486(1) = 2 (binary 10).
..........
..........
.....\2/..
...\1/.... Coded by A014486(A218779(2)) = A014486(2) = 10 (bin. 1010).
..........
..........
.\3/ \2/..
...\1/.... Coded by A014486(A218779(3)) = A014486(6) = 50 (110010).
..........
..........
..\4/.....
.\3/.\2/..
...\1/.... Coded by A014486(A218779(4)) = A014486(16) = 210 (11010010).
..........
Thus the first four terms of this sequence are 2, 10, 50 and 210.

Links

Crossrefs

a(n) = A014486(A218779(n)). Cf. A014486, A218614, A218776, A218782, A218780. A218788.

A218781 A014486-indices for the compact representation of Beanstalk-tree, with the lesser numbers coming to the left hand side.

Original entry on oeis.org

1, 2, 5, 12, 32, 92, 278, 877, 2861, 9572, 32656, 113164, 397190, 1409006, 5043617, 18194197, 66075777, 241385044, 886422017, 3270283189, 12115355601, 45052126049, 168100964161, 629171367473, 2361546968519, 8886942571534, 33523357596518, 126736969302857
Offset: 1

Views

Author

Antti Karttunen, Nov 17 2012

Keywords

Comments

See the comments and examples at A218780.

Links

Crossrefs

Cf. A218787, A218780, A218777, A218779.

Formula

a(n) = A080300(A218780(n)).

A218782 A014486-codes for the compact representation of Beanstalk-tree, growing by two natural numbers at time, starting from the tree of one internal node (1) and two leaves (3 and 2), with the larger numbers coming to the left hand side.

Original entry on oeis.org

2, 12, 52, 216, 872, 3496, 14024, 56200, 224904, 899720, 3599496, 14398600, 57599112, 230398088, 921606280, 3686471816, 14745933960, 58983782536, 235935438984, 943742064776, 3774970665096, 15099883493512, 60399541098632, 241598171519112, 966392760309896
Offset: 1

Views

Author

Antti Karttunen, Nov 17 2012

Keywords

Comments

The active middle region of the triangle (see attached "Wolframesque" illustration) corresponds to the area where the growing tip(s) of the beanstalk are located. Successively larger "turbulences" occurring in that area appear approximately at the row numbers given by A218548 divided by two. The larger tendrils, (the finite side-trees) are, the longer there is vacillation in the direction of the growing region, which lasts until the growing tip of the infinite stem (A179016) has passed the topmost tips of the tendril. See also A218612.
These are the mirror-images (in binary tree sense) of the terms in sequence A218780. For less compact versions, see A218778 & A218776.

Examples

			Illustration how the growing beanstalk-tree produces the first four terms of this sequence. In this "compact" variant, each successive pair of numbers ((2,3), (4,5), (6,7), etc.) adds a new bud (\/) to the beanstalk, with the lesser numbers coming to the right hand side:
----------
..3...2...
...\./.... Coded by A014486(A218783(1)) = A014486(1) = 2 (binary 10).
....1.....
----------
5...4.....
.\./......
..3...2...
...\./.... Coded by A014486(A218783(2)) = A014486(3) = 12 (bin. 1100).
....1.....
----------
..7...6...
...\./....
5...4.....
.\./......
..3...2...
...\./.... Coded by A014486(A218783(3)) = A014486(7) = 52 (110100).
....1.....
----------
9...8.....
.\./......
..7...6...
...\./....
5...4.....
.\./......
..3...2...
...\./.... Coded by A014486(A218783(4)) = A014486(18) = 216 (11011000).
....1.....
----------
Thus the first four terms of this sequence are 2, 12, 52 and 216.

Links

Crossrefs

a(n) = A014486(A218783(n)). Cf. A014486, A218790, A218778, A218776, A218780, A218788.
Showing 1-5 of 5 results.

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