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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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A269380 a(1) = 1, after which, for odd numbers: a(n) = A260739(n)-th number k for which A260738(k) = A260738(n)-1, and for even numbers: a(n) = a(n/2).

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 5, 1, 4, 3, 7, 2, 11, 5, 6, 1, 13, 4, 9, 3, 8, 7, 17, 2, 23, 11, 10, 5, 25, 6, 19, 1, 12, 13, 15, 4, 29, 9, 14, 3, 37, 8, 41, 7, 16, 17, 43, 2, 21, 23, 18, 11, 47, 10, 31, 5, 20, 25, 35, 6, 53, 19, 22, 1, 27, 12, 61, 13, 24, 15, 67, 4, 55, 29, 26, 9, 71, 14, 33, 3, 28, 37, 77, 8, 49, 41, 30, 7, 83, 16, 89, 17, 32, 43, 39, 2
Offset: 1

Views

Author

Antti Karttunen, Mar 01 2016

Keywords

Comments

For odd numbers n > 1, a(n) tells which term is on the immediately preceding row of A255127 (square array generated by Ludic sieve), in the same column where n itself is.

Links

Crossrefs

Cf. A255127, A260738, A260739.
Cf. A269172, A269355, A269357, A269382, A269386, A269388 (sequences that use this function).
Cf. also A268674, A269370.

Formula

a(1) = 1; after which, for even numbers a(n) = a(n/2), and for odd numbers a(n) = A255127(A260738(n)-1, A260739(n)).
Other identities. For all n >= 1:
a(A269379(n)) = n.

A269171 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A269379(a(A268674(2n+1))).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 23, 20, 21, 22, 25, 24, 19, 26, 27, 28, 29, 30, 37, 32, 33, 34, 35, 36, 41, 46, 39, 40, 43, 42, 47, 44, 45, 50, 53, 48, 31, 38, 51, 52, 61, 54, 49, 56, 57, 58, 67, 60, 71, 74, 63, 64, 65, 66, 77, 68, 69, 70, 83, 72, 89, 82, 75, 92, 59, 78, 91, 80, 81, 86, 97, 84, 79, 94, 87, 88, 107, 90, 85, 100
Offset: 1

Views

Author

Antti Karttunen, Mar 03 2016

Keywords

Links

Crossrefs

Inverse: A269172.
Cf. A000035, A003309, A008578, A055396, A078898, A268674, A255127, A269379.
Related or similar permutations: A260741, A260742, A269355, A269357, A255421, A252754, A252756, A269385, A269387.
Cf. also A269393 (a(3n)/3) and A269395.
Differs from A255407 for the first time at n=38, where a(38) = 46, while A255407(38) = 38.

Formula

a(1) = 1, then after for even n, a(n) = 2*a(n/2), and for odd n, a(n) = A269379(a(A268674(n))).
a(1) = 1, for n > 1, a(n) = A255127(A055396(n), a(A078898(n))).
As a composition of other permutations:
a(n) = A269385(A252756(n)).
a(n) = A269387(A252754(n)).
Other identities. For all n >= 1:
A000035(a(n)) = A000035(n). [Preserves the parity of n.]
a(A008578(n)) = A003309(n). [Maps noncomposites to Ludic numbers.]

A269355 Permutation of natural numbers: a(n) = A269380(A250469(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 23, 10, 11, 12, 13, 14, 15, 16, 9, 18, 17, 20, 31, 22, 25, 24, 21, 26, 27, 28, 19, 30, 29, 32, 49, 34, 71, 36, 37, 38, 39, 40, 41, 42, 43, 44, 107, 46, 47, 48, 119, 50, 51, 52, 35, 54, 89, 56, 101, 58, 53, 60, 61, 62, 63, 64, 115, 66, 67, 68, 173, 70, 55, 72, 33, 74, 75, 76, 131, 78, 77, 80, 167
Offset: 1

Views

Author

Antti Karttunen, Mar 03 2016

Keywords

Examples

			For n=9 we first find what number is below 9 in square array A083221, which is 25, then we find what number is above 25 in square array A255127, which is 23, thus a(9) = 23.

Links

Crossrefs

Inverse: A269356.
Cf. A250469, A269380.
Cf. also arrays A083221 & A255127.
More recursed variant: A269357. Cf. also permutations A266645, A255407, A269171.

Programs

Formula

a(n) = A269380(A250469(n)).
Other identities. For all n >= 1:
a(2n) = 2n. [Fixes the even numbers.]

A269358 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A268674(A269379(2n+1)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 17, 10, 11, 12, 13, 14, 15, 16, 19, 34, 29, 20, 25, 22, 9, 24, 23, 26, 27, 28, 31, 30, 21, 32, 73, 38, 53, 68, 37, 58, 39, 40, 41, 50, 43, 44, 107, 18, 47, 48, 33, 46, 51, 52, 59, 54, 71, 56, 137, 62, 101, 60, 61, 42, 63, 64, 109, 146, 67, 76, 121, 106, 35, 136, 97, 74, 75, 116, 79, 78, 131, 80, 197
Offset: 1

Views

Author

Antti Karttunen, Mar 03 2016

Keywords

Comments

This is a variant of A269356, from which it differs for the first time at n=18.

Links

Crossrefs

Inverse: A269357.
Cf. A000035, A268674, A269379, A269356, A269171.

Formula

a(1) = 1, after which, for even n, a(n) = 2*a(n/2) and for odd n, a(n) = A269356(n) = A268674(A269379(n)).
Other identities. For all n >= 1:
A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]
Showing 1-4 of 4 results.

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