A075171 -id:A075171 - cp's OEIS frontend

A075170 Sequence A075171 interpreted as binary numbers and converted to decimal.

0, 2, 10, 12, 44, 42, 50, 52, 180, 178, 170, 172, 204, 202, 210, 56, 184, 722, 714, 716, 684, 682, 690, 692, 820, 818, 810, 812, 844, 842, 226, 216, 728, 738, 2890, 2892, 2860, 2858, 2866, 2868, 2740, 2738, 2730, 2732, 2764, 2762, 2770, 696, 824, 3282

Offset: 0

Antti Karttunen, Sep 13 2002

Permutation of A014486. Same sequence shown in binary: A075171. The binary width of each term / 2 is given by A075172.

A075172 Number of edges in each rooted plane tree produced with the binary run length unranking algorithm presented in A075171.

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 4, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7

Offset: 0

Antti Karttunen, Sep 13 2002

nonn

Also the digital length of A075171(n)/ 2. Each value v occurs A000108(v) times.

Permutation of A072643.

A075166 Natural numbers mapped to Dyck path encodings of the rooted plane trees obtained by recursing on the exponents of the prime factorization of n.

Original entry on oeis.org

0, 10, 1010, 1100, 101010, 101100, 10101010, 110100, 110010, 10101100, 1010101010, 10110100, 101010101010, 1010101100, 10110010, 111000, 10101010101010, 11001100, 1010101010101010, 1010110100, 1010110010

Offset: 1

Antti Karttunen, Sep 13 2002

Note that we recurse on the exponent + 1 for all other primes except the largest one in the factorization. Thus for 6 = 3^1 * 2^1 we construct a tree by joining trees 1 and 2 with a new root node, for 7 = 7^1 * 5^0 * 3^0 * 2^0 we join four 1-trees (single leaves) with a new root node, for 8 = 2^3 we add a single edge below tree 3 and for 9 = 3^2 * 2^0 we join trees 2 and 1, to get the mirror image of tree 6. Compare to Matula/Goebel numbering of (unoriented) rooted trees as explained in A061773.

			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.....

A. Karttunen, Alternative Catalan Orderings (with the complete Scheme source)
A. Karttunen, Complete Scheme-program for computing this sequence.

Permutation of A063171. Same sequence shown in decimal: A075165. The digital length of each term / 2 (the number of o-nodes in the corresponding trees) is given by A075167. Cf. A075171, A007088.

a(n) = A007088(A075165(n)) = A106456(A106442(n)). - Antti Karttunen, May 09 2005

A075168 Position of A075170(n) in A014486.

Original entry on oeis.org

0, 1, 2, 3, 5, 4, 6, 7, 12, 11, 9, 10, 15, 14, 16, 8, 13, 30, 28, 29, 24, 23, 25, 26, 40, 39, 37, 38, 43, 42, 19, 18, 32, 33, 84, 85, 80, 79, 81, 82, 68, 67, 65, 66, 71, 70, 72, 27, 41, 114, 112, 113, 108, 107, 109, 110, 124, 123, 121, 122, 52, 51, 47, 17, 31, 89, 93, 94

Offset: 0

Antti Karttunen, Sep 13 2002

nonn

See A075171.

Inverse of A075169.

A075169 Position of A014486(n) in A075170.

Original entry on oeis.org

0, 1, 2, 3, 5, 4, 6, 7, 15, 10, 11, 9, 8, 16, 13, 12, 14, 63, 31, 30, 127, 255, 65535, 21, 20, 22, 23, 47, 18, 19, 17, 64, 32, 33, 128, 256, 65536, 26, 27, 25, 24, 48, 29, 28, 126, 2047, 4095, 62, 1023, 511, 131071, 61, 60, 254, 16383, 8191, 510, 32767

Offset: 0

Antti Karttunen, Sep 13 2002

nonn

See A075171.

Inverse of A075168.

cp's OEIS Frontend

A075170 Sequence A075171 interpreted as binary numbers and converted to decimal.

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A075172 Number of edges in each rooted plane tree produced with the binary run length unranking algorithm presented in A075171.

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A075166 Natural numbers mapped to Dyck path encodings of the rooted plane trees obtained by recursing on the exponents of the prime factorization of n.

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A075168 Position of A075170(n) in A014486.

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A075169 Position of A014486(n) in A075170.

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