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.

Showing 1-4 of 4 results.

A257264 Square array A(row,col) read by antidiagonals: A(1,col) = A055938(col), and for row > 1, A(row,col) = A011371(A(row-1,col)).

Original entry on oeis.org

2, 5, 1, 6, 3, 0, 9, 4, 1, 0, 12, 7, 3, 0, 0, 13, 10, 4, 1, 0, 0, 14, 10, 8, 3, 0, 0, 0, 17, 11, 8, 7, 1, 0, 0, 0, 20, 15, 8, 7, 4, 0, 0, 0, 0, 21, 18, 11, 7, 4, 3, 0, 0, 0, 0, 24, 18, 16, 8, 4, 3, 1, 0, 0, 0, 0, 27, 22, 16, 15, 7, 3, 1, 0, 0, 0, 0, 0, 28, 23, 19, 15, 11, 4, 1, 0, 0, 0, 0, 0, 0, 29, 25, 19, 16, 11, 8, 3, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Antti Karttunen, May 03 2015

Keywords

Comments

The array is read by antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
Column n gives the trajectory of iterates of A011371, when starting from A055938(n), thus stepping through successive parent-nodes when starting from the n-th leaf of binary beanstalk, until finally reaching the fixed point 0, which is the root of the whole binary tree.
The hanging tails of columns (upward from the first encountered zero) converge towards A179016.

Examples

			The top left corner of the array:
2, 5, 6, 9, 12, 13, 14, 17, 20, 21, 24, 27, 28, 29, 30, 33, 36, 37, 40, 43
1, 3, 4, 7, 10, 10, 11, 15, 18, 18, 22, 23, 25, 25, 26, 31, 34, 34, 38, 39
0, 1, 3, 4,  8,  8,  8, 11, 16, 16, 19, 19, 22, 22, 23, 26, 32, 32, 35, 35
0, 0, 1, 3,  7,  7,  7,  8, 15, 15, 16, 16, 19, 19, 19, 23, 31, 31, 32, 32
0, 0, 0, 1,  4,  4,  4,  7, 11, 11, 15, 15, 16, 16, 16, 19, 26, 26, 31, 31
0, 0, 0, 0,  3,  3,  3,  4,  8,  8, 11, 11, 15, 15, 15, 16, 23, 23, 26, 26
0, 0, 0, 0,  1,  1,  1,  3,  7,  7,  8,  8, 11, 11, 11, 15, 19, 19, 23, 23
0, 0, 0, 0,  0,  0,  0,  1,  4,  4,  7,  7,  8,  8,  8, 11, 16, 16, 19, 19
0, 0, 0, 0,  0,  0,  0,  0,  3,  3,  4,  4,  7,  7,  7,  8, 15, 15, 16, 16
0, 0, 0, 0,  0,  0,  0,  0,  1,  1,  3,  3,  4,  4,  4,  7, 11, 11, 15, 15
0, 0, 0, 0,  0,  0,  0,  0,  0,  0,  1,  1,  3,  3,  3,  4,  8,  8, 11, 11
0, 0, 0, 0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  1,  1,  3,  7,  7,  8,  8
0, 0, 0, 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  4,  4,  7,  7
0, 0, 0, 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  3,  3,  4,  4
0, 0, 0, 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  1,  3,  3
0, 0, 0, 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  1
...

Links

Crossrefs

Row 1: A055938, Row 2: A257507.
Cf. A011371, A055938.
Cf. also A071542, A179016, A218254, A256993, A256997, A257265.

Programs

A257508 Next-to-leaf vertices in binary beanstalk; Numbers n for which A257265(n) = 1.

Original entry on oeis.org

1, 3, 4, 7, 10, 11, 15, 18, 22, 23, 25, 26, 31, 34, 38, 39, 41, 46, 47, 49, 50, 54, 56, 57, 63, 66, 70, 71, 73, 78, 79, 81, 82, 86, 88, 94, 95, 97, 98, 102, 104, 105, 110, 113, 116, 117, 119, 120, 127, 130, 134, 135, 137, 142, 143, 145, 146, 150, 152, 158, 159, 161, 162, 166, 168, 169, 174, 177, 180, 181
Offset: 1

Views

Author

Antti Karttunen, May 03 2015

Keywords

Comments

Numbers n for which A257265(n) = 1, in other words, numbers n for which a descendant leaf nearest to n in binary beanstalk is one edge away.
Numbers n such that either A079559(A213723(n)) or A079559(A213724(n)) (or both) are zero.
Equal to A257507 with duplicate terms removed.

Examples

			3 is present because it has an immediate leaf-child 5, as A011371(5) = 3.
4 is present because it has an immediate leaf-child 6, as A011371(6) = 4.
10 is present because it has two immediate leaf-children, 12 and 13, as A011371(12) = A011371(13) = 10.
See also Paul Tek's illustration.

Links

Crossrefs

Positions of 1's in A257265.
Subsequence of A005187.
Cf. A011371, A079559, A213723, A213724, A257507, A257509, A257512 (a subsequence).

Programs

  • Haskell
    a257508 n = a257508_list !! (n-1)
a257508_list = filter ((== 1) . a257265) [0..]
-- Reinhard Zumkeller, May 06 2015

A257512 Those vertices of the binary beanstalk whose children are both leaves.

Original entry on oeis.org

10, 18, 25, 34, 41, 54, 56, 66, 73, 86, 88, 102, 110, 117, 119, 130, 137, 150, 152, 166, 174, 181, 183, 198, 206, 213, 222, 229, 243, 244, 246, 258, 265, 278, 280, 294, 302, 309, 311, 326, 334, 341, 350, 357, 371, 372, 374, 390, 398, 405, 414, 421, 435, 436, 446, 453, 467, 468, 483, 491, 498, 499, 501, 514
Offset: 1

Views

Author

Antti Karttunen, May 03 2015

Keywords

Comments

Numbers n for which both A079559(A213723(n)) and A079559(A213724(n)) are zero.
Numbers which occur twice in A257507.

Examples

			10 is present, because A011371(12) = A011371(13) = 10, and both 12 and 13 are terms of A055938. See also Paul Tek's illustration.

Links

Crossrefs

Cf. A011371, A055938, A079559, A213723, A213724, A257507, A257265.
First differences: A256490.
Subsequence of A005187, A213717 and A257508.

A262902 a(n) = A049820(A045765(n)); parent-nodes of the leaves of the tree generated by edge-relation A049820(child) = parent.

Original entry on oeis.org

5, 4, 11, 17, 14, 16, 22, 22, 29, 27, 35, 32, 41, 46, 44, 46, 51, 48, 57, 57, 58, 65, 62, 70, 69, 77, 81, 80, 92, 91, 101, 96, 107, 102, 111, 110, 111, 119, 118, 114, 129, 120, 129, 130, 128, 128, 139, 141, 138, 147, 144, 155, 148, 161, 158, 165, 152, 162, 166, 169, 162, 176, 181, 191, 187, 199, 192, 201, 214, 215, 222, 216, 227, 224, 231, 239, 238, 238, 249, 234, 249, 247, 255, 255
Offset: 1

Views

Author

Antti Karttunen, Oct 06 2015

Keywords

Comments

The sequence is computed for each leaf of the tree (A045765), ordered by their magnitude, and it contains duplicates.

Links

Crossrefs

Row 2 of A262898.
Cf. A262901 (same sequence sorted into ascending order, with duplicates removed).
Cf. A049820, A045765.
Cf. also A257507.

Programs

Formula

a(n) = A049820(A045765(n)).
Showing 1-4 of 4 results.

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