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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.

Showing 1-4 of 4 results.

A269379 a(1) = 1; for n > 1, a(n) = A255127(A260738(n)+1, A260739(n)).

Original entry on oeis.org

1, 3, 5, 9, 7, 15, 11, 21, 19, 27, 13, 33, 17, 39, 35, 45, 23, 51, 31, 57, 49, 63, 25, 69, 29, 75, 65, 81, 37, 87, 55, 93, 79, 99, 59, 105, 41, 111, 95, 117, 43, 123, 47, 129, 109, 135, 53, 141, 85, 147, 125, 153, 61, 159, 73, 165, 139, 171, 103, 177, 67, 183, 155, 189, 113, 195, 71, 201, 169, 207, 77, 213, 101, 219, 185, 225, 83
Offset: 1

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Author

Antti Karttunen, Mar 01 2016

Keywords

Comments

a(n) = the number located immediately below n in A255127 (square array generated by Ludic sieve) in the same column where n itself is, or in other words, the number removed in the next filtering stage at the same step as when n was removed in the A260738(n)-th stage.
Permutation of odd numbers.

Links

Crossrefs

Cf. A255127, A260738, A260739.
Cf. A269171, A269356, A269358, A269382, A269385, A269387 (sequences that use this function).
Cf. A269380 (left inverse).
Cf. also A250469, A269369.

Programs

Formula

a(1) = 1; for n > 1, a(n) = A255127(A260738(n)+1, A260739(n)).
Other identities. For all n >= 1:
A269380(a(n)) = n.

A269172 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(a(A269380(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, 25, 20, 21, 22, 19, 24, 23, 26, 27, 28, 29, 30, 49, 32, 33, 34, 35, 36, 31, 50, 39, 40, 37, 42, 41, 44, 45, 38, 43, 48, 55, 46, 51, 52, 47, 54, 121, 56, 57, 58, 77, 60, 53, 98, 63, 64, 65, 66, 59, 68, 69, 70, 61, 72, 169, 62, 75, 100, 67, 78, 85, 80, 81
Offset: 1

Views

Author

Antti Karttunen, Mar 03 2016

Keywords

Links

Crossrefs

Inverse: A269171.
Cf. A000035, A003309, A008578, A083221, A250469, A260738, A260739, A269380.
Related or similar permutations: A260741, A260742, A269356, A269358, A255422.
Cf. also A269394 (a(3n)/3) and A269396.
Differs from A255408 for the first time at n=38, where a(38) = 50, while A255408(38) = 38.

Formula

a(1) = 1, then after for even n, a(n) = 2*a(n/2), and for odd n, A250469(a(A269380(n))).
a(1) = 1, for n > 1, a(n) = A083221(A260738(n), a(A260739(n))).
As a composition of other permutations:
a(n) = A252755(A269386(n)).
a(n) = A252753(A269388(n)).
Other identities. For all n >= 1:
A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]
a(A003309(n)) = A008578(n). [Maps Ludic numbers to noncomposites.]

A269356 Permutation of natural numbers: a(n) = A268674(A269379(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 17, 10, 11, 12, 13, 14, 15, 16, 19, 18, 29, 20, 25, 22, 9, 24, 23, 26, 27, 28, 31, 30, 21, 32, 73, 34, 53, 36, 37, 38, 39, 40, 41, 42, 43, 44, 107, 46, 47, 48, 33, 50, 51, 52, 59, 54, 71, 56, 137, 58, 101, 60, 61, 62, 63, 64, 109, 66, 67, 68, 121, 70, 35, 72, 97, 74, 75, 76, 79, 78, 131, 80, 197
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 A255127, which is 19, then we find what number is above 19 in square array A083221, which is 17, thus a(9) = 17.

Links

Crossrefs

Inverse: A269355.
Cf. A268674, A269379.
Cf. also arrays A083221 & A255127.
More recursed variant: A269358. Cf. also permutations A266646, A255408, A269172.

Programs

Formula

a(n) = A268674(A269379(n)).
Other identities. For all n >= 1:
a(2n) = 2n. [Fixes the even numbers.]

A269357 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A269380(A250469(2n+1)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 23, 10, 11, 12, 13, 14, 15, 16, 9, 46, 17, 20, 31, 22, 25, 24, 21, 26, 27, 28, 19, 30, 29, 32, 49, 18, 71, 92, 37, 34, 39, 40, 41, 62, 43, 44, 107, 50, 47, 48, 119, 42, 51, 52, 35, 54, 89, 56, 101, 38, 53, 60, 61, 58, 63, 64, 115, 98, 67, 36, 173, 142, 55, 184, 33, 74, 75, 68, 131, 78, 77, 80, 167
Offset: 1

Views

Author

Antti Karttunen, Mar 03 2016

Keywords

Comments

This is a variant of A269355, from which it differs for the first time at n=18.

Links

Crossrefs

Inverse: A269358.
Cf. A000035, A250469, A269380, A269355, A269172.

Formula

a(1) = 1, after which, for even n, a(n) = 2*a(n/2) and for odd n, a(n) = A269355(n) = A269380(A250469(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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