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 1-3 of 3 results.

A106456 Natural numbers mapped to Dyck path encodings of the rooted plane trees obtained by recursing on the exponents of the GF(2)[X] factorization of n.

Original entry on oeis.org

0, 10, 1010, 1100, 110010, 101100, 101010, 110100, 10110010, 11001100, 10101010, 10110100, 1010101010, 10101100, 11010010, 111000, 11100010, 1011001100, 101010101010, 1100110100, 11001010, 1010101100, 101010110010
Offset: 1

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Author

Antti Karttunen, May 09 2005

Keywords

Comments

Note that we recurse on the exponent + 1 for all other irreducible polynomials except the largest one in the GF(2)[X] factorization. Thus for 6 = A048723(3,1) X A048723(2,1) we construct a tree by joining trees 1 and 2 with a new root node, for 7 = A048723(7,1) X A048723(3,0) X A048723(2,0) we join three 1-trees (single leaves) with a new root node, for 8 = A048273(2,3) we add a single edge below tree 3 and for 9 = A048723(7,1) X A048723(3,1) X A048273(2,0) we connect the trees 1 and 2 and 1 with a new root node.

Examples

			The rooted plane trees encoded here are:
.....................o....o..........o.........o...o....o.....
.....................|....|..........|..........\./.....|.....
.......o....o...o....o....o...o..o...o..o.o.o....o....o.o.o...
.......|.....\./.....|.....\./....\./....\|/.....|.....\|/....
*......*......*......*......*......*......*......*......*.....
1......2......3......4......5......6......7......8......9.....

Links

Crossrefs

a(n) = A007088(A106455(n)) = A075166(A106443(n)). GF(2)[X]-analog of A075166. Permutation of A063171. Same sequence shown in decimal: A106455. The digital length of each term / 2 (the number of o-nodes in the corresponding trees) is given by A106457. Cf. A106451-A106454.

A106453 Position of A106455(n) in A014486 plus one.

Original entry on oeis.org

1, 2, 3, 4, 7, 6, 5, 8, 12, 16, 10, 13, 24, 11, 17, 9, 20, 30, 66, 41, 15, 25, 68, 14, 198, 67, 31, 27, 26, 44, 627, 21, 2059, 53, 71, 83, 2057, 199, 73, 42, 6919, 39, 629, 69, 34, 204, 23715, 35, 29, 628, 54, 201, 200, 86, 82501, 28, 205, 72, 290513, 125, 1033413
Offset: 1

Views

Author

Antti Karttunen, May 09 2005

Keywords

Comments

See A106456.

Links

Crossrefs

Inverse: A106454. a(n) = A075163(A106443(n)). a(n) = A106451(n-1)+1. GF(2)[X]-analog of A075163.

A106452 Position of A014486(n) in A106455, minus one.

Original entry on oeis.org

0, 1, 2, 3, 6, 5, 4, 7, 15, 10, 13, 8, 11, 23, 20, 9, 14, 127, 63, 16, 31, 255, 65535, 12, 21, 28, 27, 55, 48, 17, 26, 191, 95, 44, 47, 383, 98303, 68, 41, 62, 19, 39, 106, 29, 254, 2047, 16383, 84, 511, 4095, 16777215, 272, 33, 50, 2097151, 1023, 256, 32767
Offset: 0

Views

Author

Antti Karttunen, May 09 2005

Keywords

Comments

See A106456. The next term, a(58) = 340282366920938463463374607431768211455 = (2^128) - 1 as A063171(58) = 1110101000, 11010100 = A063171(17), a(17)=127 and 127+1 = 128.

Links

Crossrefs

Inverse: A106451. a(n) = A106454(n+1)-1. GF(2)[X]-analog of A075162.
Showing 1-3 of 3 results.

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