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.

A253890 a(n) = A253560(A253883(n)) = A122111((2*A122111(n)) - 1).

Original entry on oeis.org

1, 4, 16, 8, 18, 32, 2048, 9, 128, 512, 100, 256, 2147483648, 32768, 54, 64, 1200, 1024, 10616832, 144, 1048576, 864, 43200, 25, 65536, 8796093022208, 81, 4194304, 644972544, 131072, 7260, 36, 486, 75557863725914323419136, 268435456, 8192
Offset: 1

Views

Author

Antti Karttunen, Jan 17 2015

Keywords

Comments

Conjugate the partition defined by the prime factorization of n (see, e.g., table A112798 or A241918), resulting k = A122111(n), then take the k-th odd number (2k-1), and conjugate again, giving a(n) = A122111(2k-1).
Thus after a(1)=1, this is a permutation of A070003 (numbers divisible by the square of their largest prime factor).
When A122111 is represented as a binary tree, then node A122111(t > 1) = n has as its left child A122111(2t-1) = a(n).

Crossrefs

Cf. A070003 (same sequence without 1, sorted into ascending order).
Cf. A005408, A122111, A253560, A253883.
Cf. also A112798 and A241918.

Formula

a(n) = A122111((2*A122111(n)) - 1) = A122111(A005408(A122111(n) - 1)).
a(n) = A253560(A253883(n)).

A253791 Permutation of natural numbers: a(n) = A244153(A005940(n+1)).

Original entry on oeis.org

0, 1, 2, 4, 3, 8, 32, 5, 16, 64, 256, 128, 12, 10, 16384, 512, 9, 7, 2048, 33, 257, 32768, 4194304, 8192, 8388608, 35, 8589934592, 262144, 4194305, 67108864, 260, 19, 6, 4096, 34, 18, 134217728, 2097152, 14, 1048576, 131, 4294967296, 136, 68, 295147905179352825856, 549755813888, 36028797018963968, 130, 2251799813685248, 69
Offset: 0

Views

Author

Antti Karttunen, Jan 17 2015

Keywords

Comments

When A156552 is represented as a binary tree, then for any node A156552(k) containing n larger than zero, its left child A156552(2k-1) contains 2*a(n).

Links

Crossrefs

Inverse: A253792.
Similar permutations: A253891, A253883, A005940, A244153, A156552, A054429.

Programs

Formula

a(n) = A244153(A005940(n+1)).
As a composition of other related permutations:
a(n) = A054429(A253891(A054429(n))).

A253891 Permutation of natural numbers: a(n) = A245611(A163511(n)).

Original entry on oeis.org

0, 1, 7, 3, 6, 63, 15, 2, 1023, 32767, 13, 11, 255, 511, 127, 31, 28, 507, 134217727, 8388606, 524287, 17179869183, 60, 16777215, 16383, 8388607, 65535, 510, 62, 4095, 4, 14, 1073741823, 33554429, 223, 12855504354071922204335696738729300820177623950262342682411007, 16381, 268435451, 19807040628566084398385987583, 8589934589, 55
Offset: 0

Views

Author

Antti Karttunen, Jan 17 2015

Keywords

Comments

When A243071 is represented as a binary tree, then for any node A243071(k) containing n larger than zero, its left child A243071(2k-1) contains 1+(2*a(n)).

Links

Crossrefs

Inverse: A253892.
Similar permutations: A253791, A253883, A163511, A245611, A243071, A054429.

Programs

Formula

a(n) = A245611(A163511(n)).
As a composition of other related permutations:
a(n) = A054429(A253791(A054429(n))).

A253884 Permutation of natural numbers: a(n) = A122111(A243506(n)).

Original entry on oeis.org

1, 2, 8, 4, 24, 5, 8192, 3, 64, 512, 393216, 32, 7077888, 320, 384, 6, 3802951800684688204490109616128, 15, 300578991243264, 11, 1073741824, 5184, 1134000, 128, 100, 1664, 27, 864, 392318858461667547739736838950479151006397215279002157056000, 65536, 9822276308431282926640601754292746977280, 16, 1215
Offset: 1

Views

Author

Antti Karttunen, Jan 17 2015

Keywords

Links

Crossrefs

Inverse: A253883.
Similar permutations: A253792, A253892, A122111, A243506.

Programs

Formula

a(n) = A122111(A243506(n)).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.