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 1-5 of 5 results.

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)).

A267111 Permutation of natural numbers: a(1) = 1, a(A087686(n)) = 2*a(n-1), a(A088359(n)) = 1+2*a(n), where A088359 and A087686 = numbers that occur only once (resp. more than once) in A004001, the Hofstadter-Conway $10000 sequence.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 6, 8, 9, 11, 15, 10, 13, 14, 12, 16, 17, 19, 23, 31, 18, 21, 27, 22, 29, 30, 20, 25, 26, 28, 24, 32, 33, 35, 39, 47, 63, 34, 37, 43, 55, 38, 45, 59, 46, 61, 62, 36, 41, 51, 42, 53, 54, 44, 57, 58, 60, 40, 49, 50, 52, 56, 48, 64, 65, 67, 71, 79, 95, 127, 66, 69, 75, 87, 111, 70, 77, 91, 119, 78, 93, 123
Offset: 1

Views

Author

Antti Karttunen, Jan 10 2016

Keywords

Links

Crossrefs

Inverse: A267112.
Cf. A004001, A080677, A087686, A088359, A093879, A267108, A267109.
Similar or related permutations: A006068, A054429, A276441, A233275, A233277, A276343, A276345, A276445.
Cf. also permutations A266411, A266412 and arrays A265901, A265903.

Formula

a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = 2*a(A080677(n)-1), otherwise [when n is in A088359], a(n) = 1 + 2*a(A004001(n)-1).
Equally, for n > 1, if A093879(n-1) = 0, a(n) = 2*a(n - A004001(n)), otherwise a(n) = 1 + 2*a(A004001(n)-1). [Above formula in a more symmetric form.]
As a composition of other permutations:
a(n) = A054429(A276441(n)).
a(n) = A233275(A276343(n)).
a(n) = A233277(A276345(n)).
a(n) = A006068(A276445(n)).
Other identities. For all n >= 0:
a(2^n) = 2^n. [Follows from the properties (3) and (4) of A004001 given on page 227 of Kubo & Vakil paper.]

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)).

A276443 Permutation of natural numbers: a(1) = 1, a(A087686(n)) = A000069(1+a(n-1)), a(A088359(n)) = A001969(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, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 11, 15, 13, 14, 16, 17, 18, 20, 24, 19, 23, 30, 21, 27, 25, 22, 29, 31, 26, 28, 32, 33, 34, 36, 40, 48, 35, 39, 46, 60, 37, 43, 54, 41, 51, 49, 38, 45, 58, 47, 63, 61, 42, 53, 55, 50, 44, 57, 59, 62, 52, 56, 64, 65, 66, 68, 72, 80, 96, 67, 71, 78, 92, 120, 69, 75, 86, 108, 73, 83, 102, 81
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2016

Keywords

Links

Crossrefs

Inverse: A276444.
Cf. A000069, A001969, A004001, A080677, A087686, A088359, A093879.
Similar or related permutations: A003188, A276441, A276445 (compare the scatter plots).

Programs

Formula

a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = A000069(1+a(A080677(n)-1)), otherwise [when n is in A088359], a(n) = A001969(1+a(A004001(n)-1)).
As a composition of other permutations:
a(n) = A003188(A276441(n)).

A276446 Permutation of natural numbers: a(1) = 1; a(A000069(1+n)) = A088359(a(n)), a(A001969(1+n)) = A087686(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, 11, 14, 15, 13, 8, 9, 10, 12, 20, 26, 30, 25, 31, 28, 23, 29, 16, 17, 18, 21, 19, 24, 27, 22, 37, 47, 57, 46, 62, 55, 44, 56, 63, 59, 50, 60, 41, 53, 61, 52, 32, 33, 34, 38, 35, 42, 48, 39, 36, 45, 54, 43, 58, 49, 40, 51, 70, 85, 105, 84, 120, 103, 82, 104, 126, 117, 98, 118, 79, 101, 119, 100, 127, 122, 108, 123, 89
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2016

Keywords

Links

Crossrefs

Inverse: A276445.
Cf. A000069, A001969, A004001, A010060, A087686, A088359, A115384, A245710.
Similar or related permutations: A006068, A267112, A276444.

Programs

Formula

a(1) = 1, and for n > 1, if A010060(n) = 1 [when n is one of the odious numbers, A000069], a(n) = A088359(a(A115384(n)-1)), otherwise a(n) = A087686(1+a(A245710(n))).
As a composition of other permutations:
a(n) = A267112(A006068(n)).
Showing 1-5 of 5 results.

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