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.

A243065 Permutation of natural numbers, the odd bisection of A241909 halved; equally, a composition of A064216 and A241909: a(n) = A241909(A064216(n)).

Original entry on oeis.org

1, 2, 4, 8, 3, 16, 32, 9, 64, 128, 27, 256, 6, 5, 512, 1024, 81, 18, 2048, 243, 4096, 8192, 25, 16384, 12, 729, 32768, 54, 2187, 65536, 131072, 125, 162, 262144, 6561, 524288, 1048576, 15, 36, 2097152, 7, 4194304, 486, 19683, 8388608, 108, 59049, 1458, 16777216, 625, 33554432, 67108864, 75
Offset: 1

Views

Author

Antti Karttunen, Jun 01 2014

Keywords

Comments

Are there any other fixed points than 1, 2, 18 and 72?

Links

Crossrefs

Inverse: A243066.
Cf. A064216, A241909, A243505-A243506, A244152-A244154, A243061-A243062, A006254.

Programs

Formula

a(1) = 1, and for n>=2, a(n) = A241909(2n-1)/2. Equally, a(n) = ceiling(A241909(2n-1)/2) for all n.
As a composition of related permutations:
a(n) = A241909(A064216(n)).
a(n) = A241909(A243061(A241909(n))).
For all n, a(A006254(n)) = 2^n.

A243066 Permutation of natural numbers, the even bisection of A241909 incremented by one and halved; equally, a composition of A241909 and A048673: a(n) = A048673(A241909(n)).

Original entry on oeis.org

1, 2, 5, 3, 14, 13, 41, 4, 8, 63, 122, 25, 365, 313, 38, 6, 1094, 18, 3281, 172, 188, 1563, 9842, 61, 23, 7813, 11, 1201, 29525, 123, 88574, 7, 938, 39063, 113, 39, 265721, 195313, 4688, 666, 797162, 858, 2391485, 8404, 74, 976563, 7174454, 85, 68, 88, 23438, 58825, 21523361, 28
Offset: 1

Views

Author

Antti Karttunen, Jun 01 2014

Keywords

Comments

For n > 1, 2n is found in A241909 from the position (2*a(n))-1. I.e., A241909((2*a(n))-1) = 2n for all n >= 2.
Or in other words, a(n) gives the position in the odd bisection of A241909 where 2n is located at.
Are there any other fixed points than 1, 2, 18 and 72?

Links

Crossrefs

Inverse: A243065.
Cf. A048673, A241909, A243505-A243506, A244152-A244154, A243061-A243062.

Formula

a(1) = 1, a(n) = (A241909(2*n)+1)/2.
As a composition of related permutations:
a(n) = A048673(A241909(n)).
a(n) = A241909(A243062(A241909(n))).
For all n>=1, a(2^n) = A006254(n).

A243062 Permutation of natural numbers, a composition of A048673 and A241909: a(n) = A241909(A048673(n)).

Original entry on oeis.org

1, 2, 4, 8, 3, 5, 9, 81, 64, 32, 16, 512, 6, 128, 15, 8192, 27, 6561, 25, 11, 625, 125, 18, 78125, 12, 729, 250, 45, 7, 65536, 256, 387420489, 162, 1024, 486, 1073741824, 54, 36, 16384, 2916, 243, 8388608, 49, 131072, 16807, 3125, 10, 17496, 262144, 531441, 121, 72, 75
Offset: 1

Views

Author

Antti Karttunen, Jun 02 2014

Keywords

Comments

This is A241909-conjugate of A243066. Please see the comments at the latter sequence.

Links

Crossrefs

Inverse permutation: A243061.
Cf. A048673, A241909, A243065-A243066.

Programs

Formula

a(n) = A241909(A048673(n)).
a(n) = A241909(A243066(A241909(n))).
Showing 1-3 of 3 results.

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

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