A249818 -id:A249818 - cp's OEIS frontend

A255554 Permutation of natural numbers: a(n) = A083221(A255552(n)).

1, 2, 3, 4, 9, 6, 5, 8, 7, 10, 15, 12, 11, 14, 13, 16, 21, 18, 25, 20, 17, 22, 27, 24, 19, 26, 49, 28, 33, 30, 23, 32, 29, 34, 39, 36, 31, 38, 35, 40, 45, 42, 37, 44, 121, 46, 51, 48, 41, 50, 43, 52, 57, 54, 169, 56, 77, 58, 63, 60, 55, 62, 47, 64, 69, 66, 53, 68, 59, 70, 75, 72, 61, 74, 67, 76, 81, 78, 71, 80, 65, 82, 87, 84, 289, 86, 73, 88, 93, 90, 91, 92, 79

Offset: 1

Antti Karttunen, Feb 26 2015

nonn

a(n) tells which number in array A083221, constructed from the sieve of Eratosthenes is at the same position where n is in array A255551 constructed from Lucky sieve. As both arrays have A005843 (even numbers) as their topmost row, this permutation fixes all of them.

Index entries for sequences that are permutations of the natural numbers

Inverse: A255553.
Similar permutations: A255407, A255408, A249817, A249818.
Cf. A000040, A000959, A001248, A219178, A083141, A083221, A255550, A255552.

(define (A255554 n) (A083221 (A255552 n)))

a(n) = A083221(A255552(n)).
Other identities:
a(2n) = 2n. [Fixes even numbers.]
For all n >= 1, a(A255550(n)) = A083141(n).
For all n >= 2, a(A000959(n)) = A000040(n).
For all n >= 2, a(A219178(n)) = A001248(n).

A260436 Permutation mapping from Ludic sieve to Lucky sieve: a(1) = 1, for n > 1: a(n) = A255551(A260738(n), A260739(n)).

Original entry on oeis.org

1, 2, 3, 4, 7, 6, 9, 8, 5, 10, 13, 12, 15, 14, 11, 16, 21, 18, 19, 20, 17, 22, 25, 24, 31, 26, 23, 28, 33, 30, 27, 32, 29, 34, 39, 36, 37, 38, 35, 40, 43, 42, 49, 44, 41, 46, 51, 48, 61, 50, 47, 52, 63, 54, 45, 56, 53, 58, 57, 60, 67, 62, 59, 64, 81, 66, 69, 68, 65, 70, 73, 72, 55, 74, 71, 76, 75, 78, 103, 80, 77, 82, 79, 84, 91, 86, 83, 88

Offset: 1

Antti Karttunen, Jul 30 2015

nonn

a(n) tells which number in array A255551 (constructed from Lucky sieve) is at the same position where n is in array A255127 (constructed from Ludic sieve). This permutation fixes all even numbers because both arrays have A005843 as their topmost row.

Inverse: A260435.
Cf. A000959, A003309, A255551, A260738, A260739.
Similar permutations: A255408, A255128, A255551, A255553, A249817, A249818, A260742 (a more recursed variant).

(define (A260436 n) (if (<= n 1) n (A255551bi (A260738 n) (A260739 n)))) ;; Code for A255551bi given in A255551.

Other identities. For all n >= 1:
a(A003309(n+2)) = A000959(n+1). [Maps odd Ludic numbers to Lucky numbers.]
a(2n) = 2n.
As a composition of related permutations:
a(n) = A255551(A255128(n)).
a(n) = A255553(A255408(n)).

A249810 a(1) = 0, a(n) = A078898(A003961(n)).

Original entry on oeis.org

0, 1, 1, 2, 1, 3, 1, 5, 2, 4, 1, 8, 1, 6, 3, 14, 1, 13, 1, 11, 4, 7, 1, 23, 2, 9, 9, 17, 1, 18, 1, 41, 5, 10, 3, 38, 1, 12, 6, 32, 1, 28, 1, 20, 12, 15, 1, 68, 2, 25, 7, 26, 1, 63, 4, 50, 8, 16, 1, 53, 1, 19, 19, 122, 5, 33, 1, 29, 10, 39, 1, 113, 1, 21, 17, 35, 3, 43, 1, 95, 42, 22, 1, 83, 6, 24, 11, 59, 1, 88, 4, 44, 13, 27, 7, 203

Offset: 1

Antti Karttunen, Dec 08 2014

nonn

Antti Karttunen, Table of n, a(n) for n = 1..3071

Cf. A003961, A078898, A246277, A249817, A249818, A249820, A249821, A249822, A251721, A251722, A250469, A250470.

(define (A249810 n) (if (= 1 n) 0 (A078898 (A003961 n))))

a(1) = 0, a(n) = A078898(A003961(n)).

a(1) = 0, a(n) = A078898(n) + A249820(n).

A249816 Permutation of natural numbers: a(n) = A246275(A055396(n+1), A078898(n+1)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 26, 21, 22, 23, 24, 25, 20, 27, 28, 29, 30, 31, 44, 33, 34, 35, 36, 37, 32, 39, 40, 41, 42, 43, 80, 45, 46, 47, 48, 49, 74, 51, 52, 53, 124, 55, 62, 57, 58, 59, 60, 61, 38, 63, 54, 65, 66, 67, 134, 69, 70, 71, 72, 73, 50, 75, 76, 77, 78, 79, 98, 81, 82, 83

Offset: 1

Antti Karttunen, Nov 06 2014

nonn

a(n) tells which number in square array A246275 is at the same position where n is in array A249741, the sieve of Eratosthenes minus 1. As the topmost row in both arrays is A005408 (odd numbers), they are fixed, i.e. a(2n+1) = 2n+1 for all n. Also, as the leftmost column in both arrays is primes minus one (A006093), they are also among the fixed points.

Equally: a(n) tells which number in array A246273 is at the same position where n is in the array A114881, as they are the transposes of above two arrays.

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

Inverse: A249815.
Cf. A005408, A006093, A055396, A078898, A246278.
Similar or related permutations: A250243 ("deep variant"), A246676, A249812, A249818, A246273, A246275, A114881, A249741.
Differs from A249815 and A250244 for the first time at n=32, where a(32) = 44, while A249815(32) = A250244(32) = 38.
Differs from A250244 for the first time at n=39, where a(39) = 39, while A250243(39) = 51.

(define (A249816 n) (+ -1 (A246278bi (A055396 (+ 1 n)) (A078898 (+ 1 n)))))

a(n) = A246275(A055396(n+1), A078898(n+1)).
As a composition of other permutations:
a(n) = A246676(A249812(n)).
a(n) = A249818(n+1) - 1.
Other identities. For all n >= 1:
a(A005408(n-1)) = A005408(n-1) and a(A006093(n)) = A006093(n). [Fixes odd numbers and precedents of primes. Cf. comments above].

A250248 Permutation of natural numbers: a(1) = 1, a(n) = A246278(a(A055396(n)),A078898(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 27, 22, 23, 24, 25, 26, 21, 28, 29, 30, 31, 32, 45, 34, 35, 36, 37, 38, 33, 40, 41, 42, 43, 44, 81, 46, 47, 48, 49, 50, 75, 52, 53, 54, 125, 56, 63, 58, 59, 60, 61, 62, 39, 64, 55, 66, 67, 68, 135, 70, 71, 72, 103, 74, 51, 76, 77, 78, 79, 80, 99, 82, 83

Offset: 1

Antti Karttunen, Nov 17 2014

nonn

Antti Karttunen, Table of n, a(n) for n = 1..3432
Index entries for sequences that are permutations of the natural numbers

Inverse: A250247.
Similar permutations: A250250 for even more recursed variant of A249818.
Cf. A000040, A005843, A049076, A049084, A055396, A078442, A078898, A246278.
Differs from the "vanilla version" A249818 for the first time at n=73, where a(73) = 108, while A249818(73) = 73.

a(1) = 1, a(n) = A246278(a(A055396(n)), A078898(n)).
Other identities. For all n >= 1:
a(A005843(n)) = A005843(n). [Fixes even numbers].
a(p_n) = p_{a(n)}, or equally, a(n) = A049084(a(A000040(n))). [Restriction to primes induces the same sequence].
A078442(a(n)) = A078442(n), A049076(a(n)) = A049076(n). [Preserves the "order of primeness of n"].

A260435 Permutation mapping from Lucky sieve to Ludic sieve: a(1) = 1, for n > 1: a(n) = A255127(A260438(n), A260439(n)).

Original entry on oeis.org

1, 2, 3, 4, 9, 6, 5, 8, 7, 10, 15, 12, 11, 14, 13, 16, 21, 18, 19, 20, 17, 22, 27, 24, 23, 26, 31, 28, 33, 30, 25, 32, 29, 34, 39, 36, 37, 38, 35, 40, 45, 42, 41, 44, 55, 46, 51, 48, 43, 50, 47, 52, 57, 54, 73, 56, 59, 58, 63, 60, 49, 62, 53, 64, 69, 66, 61, 68, 67, 70, 75, 72, 71, 74, 77, 76, 81, 78, 83, 80, 65, 82, 87, 84, 101, 86, 89, 88

Offset: 1

Antti Karttunen, Jul 30 2015

nonn

a(n) tells which number in array A255127 (constructed from Ludic sieve) is at the same position where n is in array A255551 (constructed from Lucky sieve). This permutation fixes all even numbers because both arrays have A005843 as their topmost row.

Inverse: A260436.
Cf. A000959, A003309, A255127, A260438, A260439.
Similar or related permutations: A255407, A255552, A255554, A249817, A249818, A260741 (a more recursed variant).

(define (A260435 n) (if (<= n 1) n (A255127bi (A260438 n) (A260439 n)))) ;; Code for A255127bi given in A255127.

Other identities. For all n >= 1:
a(A000959(n+1)) = A003309(n+2). [Maps Lucky numbers to odd Ludic numbers.]
a(2n) = 2n.
As a composition of related permutations:
a(n) = A255127(A255552(n)).
a(n) = A255407(A255554(n)).

A279350 a(n) = A046523(A279352(n)).

Original entry on oeis.org

1, 2, 4, 2, 8, 6, 16, 2, 4, 12, 32, 6, 64, 24, 12, 2, 128, 6, 256, 12, 4, 48, 512, 6, 8, 96, 36, 24, 1024, 30, 2048, 2, 12, 192, 24, 6, 4096, 384, 72, 12, 8192, 60, 16384, 48, 4, 768, 32768, 6, 16, 12, 12, 96, 65536, 6, 8, 24, 36, 1536, 131072, 30, 262144, 3072, 144, 2, 72, 120, 524288, 192, 12, 60, 1048576, 6, 2097152, 6144, 288, 384, 48, 240, 4194304, 12, 72

Offset: 1

Antti Karttunen, Dec 12 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..736

Cf. A046523, A249818, A278221, A278523, A279352, A279354.

a(n) = A046523(A279352(n)).

a(n) = A278221(A249818(n)).

A279354 a(n) = A046523(A279356(n)).

Original entry on oeis.org

1, 2, 4, 2, 8, 4, 16, 2, 6, 8, 32, 4, 64, 16, 12, 2, 128, 6, 256, 8, 6, 32, 512, 4, 12, 64, 24, 16, 1024, 12, 2048, 2, 12, 128, 36, 6, 4096, 256, 48, 8, 8192, 24, 16384, 32, 6, 512, 32768, 4, 24, 12, 30, 64, 65536, 6, 12, 16, 24, 1024, 131072, 12, 262144, 2048, 96, 2, 72, 48, 524288, 128, 12, 36, 1048576, 6, 2097152, 4096, 192, 256, 72, 96, 4194304, 8, 48, 8192

Offset: 1

Antti Karttunen, Dec 12 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..818

Cf. A046523, A249818, A278220, A278523, A279350, A279356.

a(n) = A046523(A279356(n)).

a(n) = A278220(A249818(n)).

cp's OEIS Frontend

A255554 Permutation of natural numbers: a(n) = A083221(A255552(n)).

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A260436 Permutation mapping from Ludic sieve to Lucky sieve: a(1) = 1, for n > 1: a(n) = A255551(A260738(n), A260739(n)).

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A249810 a(1) = 0, a(n) = A078898(A003961(n)).

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A249816 Permutation of natural numbers: a(n) = A246275(A055396(n+1), A078898(n+1)).

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A250248 Permutation of natural numbers: a(1) = 1, a(n) = A246278(a(A055396(n)),A078898(n)).

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A260435 Permutation mapping from Lucky sieve to Ludic sieve: a(1) = 1, for n > 1: a(n) = A255127(A260438(n), A260439(n)).

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A279350 a(n) = A046523(A279352(n)).

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A279354 a(n) = A046523(A279356(n)).

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