A249814 -id:A249814 - cp's OEIS frontend

A083221 Sieve of Eratosthenes arranged as an array and read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

2, 4, 3, 6, 9, 5, 8, 15, 25, 7, 10, 21, 35, 49, 11, 12, 27, 55, 77, 121, 13, 14, 33, 65, 91, 143, 169, 17, 16, 39, 85, 119, 187, 221, 289, 19, 18, 45, 95, 133, 209, 247, 323, 361, 23, 20, 51, 115, 161, 253, 299, 391, 437, 529, 29, 22, 57, 125, 203, 319, 377, 493, 551, 667

Offset: 2

Yasutoshi Kohmoto, Jun 05 2003

This is permutation of natural numbers larger than 1.
From Antti Karttunen, Dec 19 2014: (Start)
If we assume here that a(1) = 1 (but which is not explicitly included because outside of the array), then A252460 gives an inverse permutation. See also A249741.
For navigating in this array:
A055396(n) gives the row number of row where n occurs, and A078898(n) gives its column number, both starting their indexing from 1.
A250469(n) gives the number immediately below n, and when n is an odd number >= 3, A250470(n) gives the number immediately above n. If n is a composite, A249744(n) gives the number immediately left of n.
First cube of each row, which is {the initial prime of the row}^3 and also the first number neither a prime or semiprime, occurs on row n at position A250474(n).
(End)
The n-th row contains the numbers whose least prime factor is the n-th prime: A020639(T(n,k)) = A000040(n). - Franklin T. Adams-Watters, Aug 07 2015

			The top left corner of the array:
   2,   4,   6,    8,   10,   12,   14,   16,   18,   20,   22,   24,   26
   3,   9,  15,   21,   27,   33,   39,   45,   51,   57,   63,   69,   75
   5,  25,  35,   55,   65,   85,   95,  115,  125,  145,  155,  175,  185
   7,  49,  77,   91,  119,  133,  161,  203,  217,  259,  287,  301,  329
  11, 121, 143,  187,  209,  253,  319,  341,  407,  451,  473,  517,  583
  13, 169, 221,  247,  299,  377,  403,  481,  533,  559,  611,  689,  767
  17, 289, 323,  391,  493,  527,  629,  697,  731,  799,  901, 1003, 1037
  19, 361, 437,  551,  589,  703,  779,  817,  893, 1007, 1121, 1159, 1273
  23, 529, 667,  713,  851,  943,  989, 1081, 1219, 1357, 1403, 1541, 1633
  29, 841, 899, 1073, 1189, 1247, 1363, 1537, 1711, 1769, 1943, 2059, 2117
  ...

Transpose of A083140.
One more than A249741.
Inverse permutation: A252460.
Column 1: A000040, Column 2: A001248.
Row 1: A005843, Row 2: A016945, Row 3: A084967, Row 4: A084968, Row 5: A084969, Row 6: A084970.
Main diagonal: A083141.
First semiprime in each column occurs at A251717; A251718 & A251719 with additional criteria. A251724 gives the corresponding semiprimes for the latter. See also A251728.
Permutations based on mapping numbers between this array and A246278: A249817, A249818, A250244, A250245, A250247, A250249. See also: A249811, A249814, A249815.
Also used in the definition of the following arrays of permutations: A249821, A251721, A251722.
Cf. A002260, A004736, A004280, A020639, A038179, A055396, A078898, A138511, A249820, A249730, A249735, A249744, A250469, A250470, A250472, A250474.

lim = 11; a = Table[Take[Prime[n] Select[Range[lim^2], GCD[# Prime@ n, Product[Prime@ i, {i, 1, n - 1}]] == 1 &], lim], {n, lim}]; Flatten[Table[a[[i, n - i + 1]], {n, lim}, {i, n}]] (* Michael De Vlieger, Jan 04 2016, after Yasutoshi Kohmoto at A083140 *)

More terms from Hugo Pfoertner, Jun 13 2003

A252755 Tree of Eratosthenes, mirrored: a(0) = 1, a(1) = 2; after which, a(2n) = 2*a(n), a(2n+1) = A250469(a(n)).

Original entry on oeis.org

1, 2, 4, 3, 8, 9, 6, 5, 16, 21, 18, 25, 12, 15, 10, 7, 32, 45, 42, 55, 36, 51, 50, 49, 24, 33, 30, 35, 20, 27, 14, 11, 64, 93, 90, 115, 84, 123, 110, 91, 72, 105, 102, 125, 100, 147, 98, 121, 48, 69, 66, 85, 60, 87, 70, 77, 40, 57, 54, 65, 28, 39, 22, 13, 128, 189, 186, 235, 180, 267, 230, 203, 168, 249, 246, 305, 220, 327, 182, 187, 144

Offset: 0

Antti Karttunen, Jan 02 2015

This sequence can be represented as a binary tree. Each child to the left is obtained by doubling the parent, and each child to the right is obtained by applying A250469 to the parent:
                                     1
                                     |
                  ...................2...................
                 4                                       3
       8......../ \........9                   6......../ \........5
      / \                 / \                 / \                 / \
     /   \               /   \               /   \               /   \
    /     \             /     \             /     \             /     \
  16       21         18       25         12       15         10       7
32  45   42  55     36  51   50  49     24  33   30  35     20  27   14 11
etc.
Sequence A252753 is the mirror image of the same tree. A253555(n) gives the distance of n from 1 in both trees.

Antti Karttunen, Table of n, a(n) for n = 0..8192
Antti Karttunen, Entanglement Permutations, 2016-2017
Index entries for sequences that are permutations of the natural numbers

Inverse: A252756.
Row sums: A253787, products: A253788.
Similar permutations: A163511, A252753, A054429, A163511, A250245, A269865.
Cf. also: A249814 (Compare the scatterplots).
Cf. A083221, A250469, A253555.

(* b = A250469 *) b[1] = 1; b[n_] := If[PrimeQ[n], NextPrime[n], m1 = p1 = FactorInteger[n][[1, 1]]; For[k1 = 1, m1 <= n, m1 += p1; If[m1 == n, Break[]]; If[FactorInteger[m1][[1, 1]] == p1, k1++]]; m2 = p2 = NextPrime[p1]; For[k2 = 1, True, m2 += p2, If[FactorInteger[m2][[1, 1]] == p2, k2++]; If[k1 + 2 == k2, Return[m2]]]];
a[0] = 1; a[1] = 2; a[n_] := a[n] = If[EvenQ[n], 2 a[n/2], b[a[(n-1)/2]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Mar 08 2016 *)

a(0) = 1, a(1) = 2; after which, a(2n) = 2*a(n), a(2n+1) = A250469(a(n)).
As a composition of related permutations:
a(n) = A252753(A054429(n)).
a(n) = A250245(A163511(n)).

A246684 "Caves of prime shift" permutation: a(1) = 1, a(n) = A242378(A007814(n), 2*a(A003602(n))) - 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 7, 6, 9, 14, 15, 24, 13, 26, 11, 10, 17, 20, 27, 34, 29, 80, 47, 48, 25, 32, 51, 124, 21, 44, 19, 12, 33, 74, 39, 54, 53, 98, 67, 76, 57, 104, 159, 624, 93, 404, 95, 120, 49, 50, 63, 64, 101, 152, 247, 342, 41, 38, 87, 174, 37, 62, 23, 16, 65, 56, 147, 244, 77, 188, 107, 90, 105, 374, 195, 324, 133, 170, 151, 142, 113, 92

Offset: 1

Antti Karttunen, Sep 06 2014

See the comments in A246676. This is otherwise similar permutation, except that after having reached an odd number 2m-1 when we have shifted the binary representation of n right k steps, here, in contrary to A246676, we don't shift the primes in the prime factorization of the even number 2m, but instead of an even number (2*a(m)), shifting it the same number (k) of positions towards larger primes, whose product is then decremented by one to get the final result.
From Antti Karttunen, Jan 18 2015: (Start)
This can be viewed as an entanglement or encoding permutation where the complementary pairs of sequences to be interwoven together are even and odd numbers (A005843/A005408) which are entangled with another complementary pair: even numbers in the order they appear in A253885 and odd numbers in their usual order: (A253885/A005408).
From the above follows also that this sequence can be represented as a binary tree. Each child to the left is obtained by doubling the parent and subtracting one, and each child to the right is obtained by applying A253885 to the parent:
                                      1
                                      |
                   ...................2...................
                  3                                       4
        5......../ \........8                   7......../ \........6
       / \                 / \                 / \                 / \
      /   \               /   \               /   \               /   \
     /     \             /     \             /     \             /     \
    9       14         15       24         13       26         11       10
  17 20   27  34     29  80   47  48     25  32   51  124    21  44   19  12
(End)

			Consider n=30, "11110" in binary. It has to be shifted just one bit-position right that the result were an odd number 15, "1111" in binary. As 15 = 2*8-1, we use 2*a(8) = 2*6 = 12 = 2*2*3 = p_1 * p_1 * p_2 [where p_k denotes the k-th prime, A000040(k)], which we shift one step towards larger primes resulting p_2 * p_2 * p_3 = 3*3*5 = 45, thus a(30) = 45-1 = 44.

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences that are permutations of the natural numbers

Inverse: A246683.
Other versions: A246676, A246678.
Similar or related permutations: A005940, A163511, A241909, A245606, A246278, A246375, A249814, A250243.
Cf. A000040, A000051, A003602, A003961, A007814, A242378, A253885.
Differs from A249814 for the first time at n=14, where a(14) = 26, while A249814(14) = 20.

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of Michel Marcus
A246684(n) = { my(k=0); if(1==n, 1, while(!(n%2), n = n/2; k++); n = 2*A246684((n+1)/2); while(k>0, n = A003961(n); k--); n-1); };
for(n=1, 8192, write("b246684.txt", n, " ", A246684(n)));
(Scheme, with memoization-macro definec, two implementations)
(definec (A246684 n) (cond ((<= n 1) n) (else (+ -1 (A242378bi (A007814 n) (* 2 (A246684 (A003602 n)))))))) ;; Code for A242378bi given in A242378.
(definec (A246684 n) (cond ((<= n 1) n) ((even? n) (A253885 (A246684 (/ n 2)))) (else (+ -1 (* 2 (A246684 (/ (+ n 1) 2)))))))

a(1) = 1, a(n) = A242378(A007814(n), 2*a(A003602(n))) - 1. [Where the bivariate function A242378(k,n) changes each prime p(i) in the prime factorization of n to p(i+k), i.e., it's the result of A003961 iterated k times starting from n].
a(1) = 1, a(2n) = A253885(a(n)), a(2n+1) = (2*a(n+1))-1. - Antti Karttunen, Jan 18 2015
As a composition of other permutations:
a(n) = A250243(A249814(n)).
Other identities. For all n >= 1, the following holds:
a(n) = (1+a((2*n)-1))/2. [The odd bisection from a(1) onward with one added and then halved gives the sequence back].
For all n >= 0, the following holds: a(A000051(n)) = A000051(n). [Numbers of the form 2^n + 1 are among the fixed points].

A250244 Permutation of natural numbers: a(n) = A249741(A055396(n+1), a(A246277(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, 38, 33, 34, 35, 36, 37, 62, 51, 40, 41, 42, 43, 32, 45, 46, 47, 48, 49, 74, 39, 52, 53, 64, 55, 98, 57, 58, 59, 60, 61, 56, 75, 94, 65, 66, 67, 110, 69, 70, 71, 72, 73, 50, 123, 76, 101, 78, 79, 44, 81, 82, 83, 154, 85, 134, 63, 88, 89

Offset: 1

Antti Karttunen, Nov 16 2014

nonn

This is a "more recursed" variant of A249815. Preserves the parity of n.

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences that are permutations of the natural numbers

Inverse: A250243.
Cf. A006093, A055396, A083221, A246277, A249741.
Similar or related permutations: A246683, A249814, A250245.
Differs from A249816 and A250243 for the first time at n=32, where a(32) = 38, while A249816(32) = A250243(32) = 44.
Differs from the "shallow variant" A249815 for the first time at n=39, where a(39) = 51, while A249815(39) = 39

a(n) = A249741(A055396(n+1), a(A246277(n+1))).
As a composition of other permutations:
a(n) = A249814(A246683(n)).
Other identities. For all n >= 1, the following holds:
a(n) = (1+a((2*n)-1)) / 2. [The odd bisection from a(1) onward with one added and then halved gives the sequence back.]
a(A006093(n)) = A006093(n). [Primes minus one are among the fixed points].

A249811 Permutation of natural numbers: a(n) = A249741(A001511(n), A003602(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 7, 6, 9, 14, 11, 24, 13, 20, 15, 10, 17, 26, 19, 34, 21, 32, 23, 48, 25, 38, 27, 54, 29, 44, 31, 12, 33, 50, 35, 64, 37, 56, 39, 76, 41, 62, 43, 84, 45, 68, 47, 120, 49, 74, 51, 94, 53, 80, 55, 90, 57, 86, 59, 114, 61, 92, 63, 16, 65, 98, 67, 124, 69, 104, 71, 118, 73, 110, 75, 144, 77, 116, 79, 142, 81

Offset: 1

Antti Karttunen, Nov 06 2014

nonn

In the essence, a(n) tells which number in square array A249741 (the sieve of Eratosthenes minus 1) is at the same position where n is in array A135764, which is formed from odd numbers whose binary expansions are shifted successively leftwards on the successive rows. As the topmost row in both arrays is A005408 (odd numbers), they are fixed, i.e., a(2n+1) = 2n+1 for all n.

Equally: a(n) tells which number in array A114881 is at the same position where n is in the array A054582, as they are the transposes of above two arrays.

Antti Karttunen, Table of n, a(n) for n = 1..8191
Index entries for sequences that are permutations of the natural numbers

Inverse: A249812.
Cf. A000079, A000265, A001511, A003602, A005408, A006093, A007814, A054582, A083140, A083221, A249741.
Similar or related permutations: A249814 ("deep variant"), A246676, A249815, A114881, A209268, A249725, A249741.
Differs from A246676 for the first time at n=14, where a(14)=20, while
A246676(14)=26.

(define (A249811 n) (+ -1 (A083221bi (A001511 n) (A003602 n))))
;; Code for A083221bi given in A083221

In the following formulas, A083221 and A249741 are interpreted as bivariate functions:
a(n) = A083221(A001511(n),A003602(n)) - 1 = A249741(A001511(n),A003602(n)).
As a composition of related permutations:
a(n) = A114881(A209268(n)).
a(n) = A249741(A249725(n)).
a(n) = A249815(A246676(n)).
Other identities. For all n >= 1 the following holds:
a(A000079(n-1)) = A006093(n).

A249813 Permutation of natural numbers: a(1) = 1, a(n) = A000079(A055396(n+1)-1) * ((2 * a(A078898(n+1))) - 1).

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 7, 6, 9, 16, 15, 32, 13, 10, 11, 64, 17, 128, 31, 14, 29, 256, 63, 12, 25, 18, 19, 512, 21, 1024, 127, 30, 33, 20, 255, 2048, 61, 26, 27, 4096, 57, 8192, 511, 22, 125, 16384, 23, 24, 49, 34, 35, 32768, 37, 28, 1023, 62, 41, 65536, 2047, 131072, 253, 58, 59, 36, 65, 262144, 39, 126, 509, 524288, 4095, 1048576, 121, 50, 51, 40, 53

Offset: 1

Antti Karttunen, Nov 06 2014

nonn

This sequence is a "recursed variant" of A249812.

See also the comments at the inverse permutation A249814.

Antti Karttunen, Table of n, a(n) for n = 1..1024
Index entries for sequences that are permutations of the natural numbers

Inverse: A249814.
Similar or related permutations: A246683, A249812, A250243.
Cf. A000079, A006093, A055396, A078898.
Differs from A246683 for the first time at n=20, where a(20) = 14, while A246683(20) = 18.

a(1) = 1, a(n) = A000079(A055396(n+1)-1) * ((2 * a(A078898(n+1))) - 1).
As a composition of other permutations:
a(n) = A246683(A250243(n)).
Other identities. For all n >= 1, the following holds:
a(n) = (1+a((2*n)-1))/2. [The odd bisection from a(1) onward with one added and then halved gives the sequence back.]
a(A006093(n)) = A000079(n-1).

A269865 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(1+a(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 9, 8, 7, 10, 15, 12, 11, 18, 27, 16, 25, 14, 21, 20, 13, 30, 45, 24, 17, 22, 33, 36, 23, 54, 81, 32, 19, 50, 75, 28, 35, 42, 63, 40, 55, 26, 39, 60, 37, 90, 135, 48, 49, 34, 51, 44, 29, 66, 99, 72, 41, 46, 69, 108, 91, 162, 243, 64, 85, 38, 57, 100, 125, 150, 225, 56, 31, 70, 105, 84, 47, 126, 189, 80, 43, 110, 165, 52

Offset: 1

Antti Karttunen, Mar 12 2016

This sequence can be represented as a binary tree. When the parent contains n, the left hand child contains 2n, while the value of right hand child is obtained by applying A250469(1+n):
                                    1
                                    |
                 ................../ \..................
                2                                       3
      4......../ \........5                   6......../ \........9
     / \                 / \                 / \                 / \
    /   \               /   \               /   \               /   \
   /     \             /     \             /     \             /     \
  8       7          10       15         12       11         18       27
16 25   14 21      20  13   30  45     24  17   22  33     36  23   54  81
etc.
Note how all nodes with odd n have a right hand child with value 3n.

Antti Karttunen, Table of n, a(n) for n = 1..6142
Antti Karttunen, Entanglement Permutations, 2016-2017
Index entries for sequences that are permutations of the natural numbers

Inverse: A269866.
Cf. A250469.
Related or similar permutations: A269359, A269863, A269864, A269867, A246375, A249814, A252755, A270195.

a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(1+a(n)).

A253886 Permutation of even numbers: a(n) = A250469(n+1) - 1.

Original entry on oeis.org

0, 2, 4, 8, 6, 14, 10, 20, 24, 26, 12, 32, 16, 38, 34, 44, 18, 50, 22, 56, 54, 62, 28, 68, 48, 74, 64, 80, 30, 86, 36, 92, 84, 98, 76, 104, 40, 110, 94, 116, 42, 122, 46, 128, 114, 134, 52, 140, 120, 146, 124, 152, 58, 158, 90, 164, 144, 170, 60, 176, 66, 182, 154, 188, 118, 194, 70, 200, 174, 206, 72, 212, 78, 218, 184, 224, 142, 230, 82

Offset: 0

Antti Karttunen, Jan 18 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 0..5000

Cf. A250469, A253885, A249814.

(define (A253886 n) (- (A250469 (+ n 1)) 1))

a(n) = A250469(n+1) - 1.

A269374 Permutation of natural numbers: a(1) = 1, a(n) = A255551(A001511(n), a(A003602(n))) - 1.

Original entry on oeis.org

1, 2, 3, 6, 5, 4, 11, 8, 9, 10, 7, 18, 21, 28, 15, 12, 17, 22, 19, 38, 13, 16, 35, 26, 41, 58, 55, 102, 29, 40, 23, 14, 33, 46, 43, 80, 37, 52, 75, 56, 25, 34, 31, 60, 69, 100, 51, 44, 81, 118, 115, 206, 109, 160, 203, 152, 57, 82, 79, 144, 45, 64, 27, 20, 65, 94, 91, 164, 85, 124, 159, 120, 73, 106, 103, 186, 149, 220, 111, 96, 49

Offset: 1

Antti Karttunen, Mar 01 2016

Permutation obtained from the Lucky sieve.
This sequence can be represented as a binary tree. For n > 2, each left hand child is obtained by doubling the contents of the parent node and subtracting one, and each right hand child is obtained by applying A269372(n), when the parent node contains n:
                                    1
                                    |
                 ...................2...................
                3                                       6
      5......../ \........4                  11......../ \........8
     / \                 / \                 / \                 / \
    /   \               /   \               /   \               /   \
   /     \             /     \             /     \             /     \
  9       10          7       18         21       28         15       12
17 22   19  38      13 16   35  26     41  58   55  102    29  40   23  14
etc.

Antti Karttunen, Table of n, a(n) for n = 1..4096
Index entries for sequences that are permutations of the natural numbers

Inverse: A269373.
Cf. A000035, A001511, A003602, A255551, A269372.
Cf. also A269375, A269377 and also A249814, A269384.

a(1) = 1, a(n) = A255551(A001511(n), a(A003602(n))) - 1.
a(1) = 1, a(2n) = A269372(a(n)), a(2n+1) = (2*a(n+1))-1.
Other identities. For all n >= 0:
A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]

A269384 Permutation of natural numbers: a(1) = 1, a(n) = A255127(A001511(n), a(A003602(n))) - 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 7, 6, 9, 14, 15, 18, 13, 20, 11, 10, 17, 26, 27, 34, 29, 44, 35, 30, 25, 38, 39, 48, 21, 32, 19, 12, 33, 50, 51, 64, 53, 80, 67, 58, 57, 86, 87, 108, 69, 104, 59, 54, 49, 74, 75, 94, 77, 116, 95, 84, 41, 62, 63, 78, 37, 56, 23, 16, 65, 98, 99, 124, 101, 152, 127, 112, 105, 158, 159, 198, 133, 200

Offset: 1

Antti Karttunen, Mar 01 2016

Permutation obtained from the Ludic sieve.
This sequence can be represented as a binary tree. For n > 2, each left hand child is obtained by doubling the contents of the parent node and subtracting one, and each right hand child is obtained by applying A269382(n), when the parent node contains n:
                                    1
                                    |
                 ...................2...................
                3                                       4
      5......../ \........8                   7......../ \........6
     / \                 / \                 / \                 / \
    /   \               /   \               /   \               /   \
   /     \             /     \             /     \             /     \
  9       14         15       18         13       20         11       10
17 26   27  34     29  44   35  30     25  38   39  48     21  32   19  12
etc.

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences that are permutations of the natural numbers

Inverse: A269383.
Cf. A000035, A001511, A003602, A255127, A269382.
Cf. also A269385, A269387 and also A249814, A269374.

a(1) = 1, a(n) = A255127(A001511(n), a(A003602(n))) - 1.
a(1) = 1, a(2n) = A269382(a(n)), a(2n+1) = (2*a(n+1))-1.
Other identities. For all n >= 0:
A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]

cp's OEIS Frontend

A083221 Sieve of Eratosthenes arranged as an array and read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A252755 Tree of Eratosthenes, mirrored: a(0) = 1, a(1) = 2; after which, a(2n) = 2*a(n), a(2n+1) = A250469(a(n)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A246684 "Caves of prime shift" permutation: a(1) = 1, a(n) = A242378(A007814(n), 2*a(A003602(n))) - 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

A250244 Permutation of natural numbers: a(n) = A249741(A055396(n+1), a(A246277(n+1))).

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A249811 Permutation of natural numbers: a(n) = A249741(A001511(n), A003602(n)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Scheme

Formula

A249813 Permutation of natural numbers: a(1) = 1, a(n) = A000079(A055396(n+1)-1) * ((2 * a(A078898(n+1))) - 1).

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A269865 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(1+a(n)).

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A253886 Permutation of even numbers: a(n) = A250469(n+1) - 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Scheme

Formula

A269374 Permutation of natural numbers: a(1) = 1, a(n) = A255551(A001511(n), a(A003602(n))) - 1.

Views

Author

Keywords