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.

A269391 Permutation of natural numbers: a(1) = 1, a(A233271(1+n)) = 2*a(n), a(A269390(n)) = 1 + 2*a(n), where A233271 is the infinite trunk of inverted binary beanstalk and A269390 is its complement.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 6, 8, 9, 11, 15, 10, 13, 17, 14, 12, 19, 23, 31, 21, 16, 27, 35, 18, 29, 25, 39, 22, 47, 63, 30, 20, 43, 33, 55, 71, 37, 26, 59, 51, 79, 34, 45, 95, 127, 28, 61, 41, 24, 87, 67, 111, 38, 143, 75, 46, 53, 119, 103, 62, 159, 69, 42, 32, 91, 191, 255, 57, 123, 83, 54, 49, 175, 135, 70, 223, 77, 287, 36
Offset: 1

Views

Author

Antti Karttunen, Mar 05 2016

Keywords

Links

Crossrefs

Inverse: A269392.
Cf. A233271, A269381, A269390.
Cf. also A260431.
Similar or related permutations: A269397, A269401.

Formula

a(1) = 1, for n > 1, if A269381(n) - A269381(n-1) > 0 [when n is in A233271] a(n) = 2*a(A269381(n)-1), otherwise a(n) = 1 + 2*a(n-A269381(n)).
As a composition of other permutations:
a(n) = A269401(A269397(n)).

A269390 Complement of A233271.

Original entry on oeis.org

3, 5, 6, 9, 10, 11, 13, 14, 17, 18, 19, 20, 22, 23, 25, 26, 27, 29, 30, 33, 34, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 50, 51, 52, 54, 55, 57, 58, 59, 61, 62, 65, 66, 67, 68, 69, 70, 72, 73, 74, 76, 77, 78, 80, 81, 83, 84, 85, 86, 88, 89, 91, 92, 93, 95, 96, 98, 99, 100, 101, 103, 104, 105, 107, 108, 109, 111
Offset: 1

Views

Author

Antti Karttunen, Mar 05 2016

Keywords

Links

Crossrefs

Cf. A233271 (complement).
Cf. A269381.
Cf. also A213713, A269391, A269392.

A269397 Permutation of natural numbers: a(1) = 1, a(A233271(1+n)) = A179016(1+a(n)), a(A269390(n)) = A213713(a(n)), where A179016, A233271 are the infinite trunks of binary beanstalk and inverted binary beanstalk and A213713, A269390 their complements.

Original entry on oeis.org

1, 3, 2, 7, 6, 5, 4, 16, 13, 12, 10, 15, 9, 27, 11, 8, 22, 21, 18, 25, 46, 17, 43, 35, 20, 14, 36, 32, 34, 29, 26, 42, 40, 69, 28, 65, 54, 23, 33, 24, 55, 85, 50, 52, 45, 31, 41, 62, 19, 60, 100, 44, 67, 95, 80, 64, 37, 51, 38, 53, 82, 122, 78, 158, 75, 77, 68, 48, 61, 91, 49, 30, 88, 143, 145, 66, 98, 136, 116, 115, 93, 63, 56, 76, 58, 79, 39
Offset: 1

Views

Author

Antti Karttunen, Mar 05 2016

Keywords

Links

Crossrefs

Inverse: A269398.
Cf. A179016, A213713, A233271, A269381, A269390.
Related or similar permutations: A269391, A269401, A269402.
Cf. also A233270.

Formula

a(1) = 1, for n > 1, if A269381(n) - A269381(n-1) > 0 [when n is in A233271] a(n) = A179016(1+a(A269381(n)-1)), otherwise a(n) = A213713(a(n-A269381(n))).
As a composition of related permutations:
a(n) = A269402(A269391(n)).

A269371 Least monotonic left inverse of A179016.

Original entry on oeis.org

0, 1, 1, 2, 3, 3, 3, 4, 5, 5, 5, 6, 6, 6, 6, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 11, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 21, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 27, 27, 27, 27, 28
Offset: 0

Views

Author

Antti Karttunen, Mar 05 2016

Keywords

Comments

a(n) = number of nonzero terms of A179016 <= n.
Partial sums of A213719 from its term A213719(1) onward (A213719(0)=1 not included).

Links

Crossrefs

Cf. A179016, A213718, A213719.
Cf. also A071542, A269381, A269401.

Formula

a(0) = 0, for n > 0, a(n) = a(n-1) + A213719(n).
a(n) = A213718(n+1) - 1.
Other identities. For all n >= 0:
a(A179016(n)) = 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.