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.

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A276441 Permutation of natural numbers: a(1) = 1, a(A087686(1+n)) = 1 + 2*a(n), a(A088359(n)) = 2*a(n), where A088359 & A087686 = numbers that occur only once & more than once in A004001.

Original entry on oeis.org

1, 3, 2, 7, 6, 4, 5, 15, 14, 12, 8, 13, 10, 9, 11, 31, 30, 28, 24, 16, 29, 26, 20, 25, 18, 17, 27, 22, 21, 19, 23, 63, 62, 60, 56, 48, 32, 61, 58, 52, 40, 57, 50, 36, 49, 34, 33, 59, 54, 44, 53, 42, 41, 51, 38, 37, 35, 55, 46, 45, 43, 39, 47, 127, 126, 124, 120, 112, 96, 64, 125, 122, 116, 104, 80, 121, 114, 100, 72, 113, 98
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2016

Keywords

Links

Crossrefs

Inverse: A276442.
Cf. A000079, A000225, A004001, A080677, A087686, A088359, A093879.
Related or similar permutations: A006068, A054429, A233275, A233277, A267111, A276343, A276345, A276443.
Cf. also arrays A265901, A265903.

Programs

Formula

a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = 1 + 2*a(A080677(n)-1), otherwise [when n is in A088359], a(n) = 2*a(A004001(n)-1).
As a composition of other permutations:
a(n) = A054429(A267111(n)).
a(n) = A233277(A276343(n)).
a(n) = A233275(A276345(n)).
a(n) = A006068(A276443(n)).
Other identities. For all n >= 1:
a(A000079(n-1)) = A000225(n).

A276445 Permutation of natural numbers: a(1) = 1, a(A087686(n)) = A001969(1+a(n-1)), a(A088359(n)) = A000069(1+a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001, and A000069 & A001969 are odious & evil numbers.

Original entry on oeis.org

1, 3, 2, 6, 7, 4, 5, 12, 13, 14, 8, 15, 11, 9, 10, 24, 25, 26, 28, 16, 27, 31, 22, 29, 19, 17, 30, 21, 23, 18, 20, 48, 49, 50, 52, 56, 32, 51, 55, 62, 44, 53, 59, 38, 57, 35, 33, 54, 61, 42, 63, 47, 45, 58, 37, 39, 34, 60, 41, 43, 46, 36, 40, 96, 97, 98, 100, 104, 112, 64, 99, 103, 110, 124, 88, 101, 107, 118, 76, 105, 115, 70
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2016

Keywords

Links

Crossrefs

Inverse: A276446.
Cf. A000069, A001969, A004001, A080677, A087686, A088359, A093879.
Similar or related permutations: A003188, A267111, A276443 (compare the scatter plots).

Programs

Formula

a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = A001969(1+a(A080677(n)-1)), otherwise [when n is in A088359], a(n) = A000069(1+a(A004001(n)-1)).
As a composition of other permutations:
a(n) = A003188(A267111(n)).

A276343 Permutation of natural numbers: a(1) = 1, a(A087686(1+n)) = A005187(1+a(n)), a(A088359(n)) = A055938(a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001.

Original entry on oeis.org

1, 3, 2, 7, 6, 5, 4, 15, 14, 13, 12, 11, 9, 10, 8, 31, 30, 29, 28, 27, 26, 24, 20, 25, 21, 23, 22, 17, 18, 19, 16, 63, 62, 61, 60, 59, 58, 57, 55, 51, 43, 56, 52, 44, 54, 48, 53, 50, 45, 36, 47, 37, 39, 49, 40, 41, 46, 42, 33, 34, 35, 38, 32, 127, 126, 125, 124, 123, 122, 121, 120, 118, 114, 106, 90, 119, 115, 107, 91, 117, 111, 99
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2016

Keywords

Links

Crossrefs

Inverse: A276344.
Cf. A004001, A005187, A055938, A080677, A087686, A088359, A093879.
Similar or related permutations: A233276, A233278, A267111, A276345, A276441.
Compare also to the scatter-plots of A276443 and A276445.

Programs

Formula

a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = A005187(1+a(A080677(n)-1)), otherwise [when n is in A088359], a(n) = A055938(a(A004001(n)-1)).
As a composition of other permutations:
a(n) = A233276(A267111(n)).
a(n) = A233278(A276441(n)).

A276345 Permutation of natural numbers: a(1) = 1, a(A087686(1+n)) = A055938(a(n)), a(A088359(n)) = A005187(1+a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001.

Original entry on oeis.org

1, 2, 3, 5, 4, 7, 6, 12, 10, 8, 15, 9, 11, 14, 13, 27, 23, 19, 16, 31, 21, 18, 22, 17, 26, 30, 20, 25, 24, 29, 28, 58, 53, 46, 38, 32, 63, 48, 41, 35, 42, 40, 34, 50, 33, 57, 62, 44, 39, 49, 37, 47, 45, 36, 56, 55, 61, 43, 54, 52, 51, 60, 59, 121, 113, 104, 89, 74, 64, 127, 108, 95, 81, 70, 82, 93, 79, 67, 98, 77, 66, 112, 65, 120
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2016

Keywords

Links

Crossrefs

Inverse: A276346.
Cf. A004001, A005187, A055938, A080677, A087686, A088359, A093879.
Similar or related permutations: A233276, A233278, A267111, A276343, A276441.

Programs

Formula

a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = A055938(a(A080677(n)-1)), otherwise [when n is in A088359], a(n) = A005187(1+a(A004001(n)-1)).
As a composition of other permutations:
a(n) = A233276(A276441(n)).
a(n) = A233278(A267111(n)).

A286539 Restricted growth sequence of A286538.

Original entry on oeis.org

1, 1, 2, 1, 3, 4, 2, 1, 3, 5, 6, 3, 5, 4, 2, 1, 3, 5, 7, 8, 3, 9, 10, 5, 7, 6, 3, 5, 5, 4, 2, 1, 3, 5, 7, 11, 12, 3, 9, 13, 14, 5, 13, 14, 7, 11, 8, 3, 9, 10, 9, 13, 10, 5, 7, 7, 6, 3, 5, 5, 5, 4, 2, 1, 3, 5, 7, 11, 15, 16, 3, 9, 13, 17, 18, 5, 13, 19, 20, 7, 17, 18, 11, 15, 12, 3, 9, 13, 14, 9, 21, 19, 13, 19, 14, 5, 13, 14, 13, 17, 14, 7, 11, 11, 8, 3, 9, 10
Offset: 1

Views

Author

Antti Karttunen, May 17 2017

Keywords

Links

Crossrefs

Cf. A267111, A286537, A286538, A286617, A286619, A278222.

A269851 a(0) = 1, a(A087686(1+n)) = 2*a(n), a(A088359(n)) = A250469(a(n)), where A088359 and A087686 = numbers that occur only once (resp. more than once) in A004001.

Original entry on oeis.org

1, 2, 4, 3, 8, 9, 5, 6, 16, 21, 25, 7, 18, 15, 10, 12, 32, 45, 55, 49, 11, 42, 51, 35, 50, 27, 14, 36, 33, 30, 20, 24, 64, 93, 115, 91, 121, 13, 90, 123, 125, 77, 110, 147, 65, 98, 39, 22, 84, 105, 85, 102, 87, 70, 100, 57, 54, 28, 72, 69, 66, 60, 40, 48, 128, 189, 235, 203, 187, 169, 17, 186, 267, 305, 217, 143, 230
Offset: 0

Views

Author

Antti Karttunen, Mar 07 2016

Keywords

Comments

Permutation of natural numbers obtained from the sieve of Eratosthenes, combined with the permutation obtained from Hofstadter-Conway $10000 sequence (A004001). Note the indexing: Domain starts from 0, range from 1.

Links

Crossrefs

Inverse: A269852.
Cf. A004001, A087686, A088359, A093879, A250469.
Related or similar permutations: A252755, A267111, A269855.

Formula

a(0) = 1, a(1) = 2, for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = 2*a(n - A004001(n)), otherwise [when n is in A088359], a(n) = A250469(a(A004001(n)-1)).
As a composition of related permutations:
a(n) = A252755(A267111(n)).
Other identities. For all n >= 0:
a(2^n) = 2^(n+1).

A286536 a(n) = A278222(A276445(n)).

Original entry on oeis.org

2, 4, 2, 4, 8, 2, 6, 4, 12, 8, 2, 16, 12, 6, 6, 4, 12, 12, 8, 2, 36, 32, 12, 24, 12, 6, 16, 30, 24, 6, 6, 4, 12, 12, 12, 8, 2, 36, 72, 32, 12, 60, 72, 12, 24, 12, 6, 36, 48, 30, 64, 48, 60, 24, 30, 24, 6, 16, 30, 60, 24, 6, 6, 4, 12, 12, 12, 12, 8, 2, 36, 72, 72, 32, 12, 60, 180, 72, 12, 60, 72, 12, 24, 12, 6, 36
Offset: 1

Views

Author

Antti Karttunen, May 17 2017

Keywords

Links

Crossrefs

Cf. A267111, A276445, A278219, A278222, A286538.
Cf. A286537 (rgs-version of this sequence).

Programs

Formula

a(n) = A278222(A276445(n)).
a(n) = A278219(A267111(n)).
Previous Showing 11-17 of 17 results.

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