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 1-4 of 4 results.

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

Views

Author

Antti Karttunen, Mar 12 2016

Keywords

Comments

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.

Links

Crossrefs

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

Formula

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

A269863 Permutation of natural numbers: a(1) = 1, a(A269360(n)) = 2*a(n), a(A250469(1+n)) = 1 + 2*a(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 9, 10, 7, 8, 13, 18, 17, 26, 11, 12, 37, 34, 25, 74, 19, 20, 69, 50, 21, 14, 15, 16, 41, 138, 33, 82, 27, 36, 53, 22, 277, 66, 35, 52, 45, 554, 105, 90, 23, 24, 1109, 210, 101, 42, 75, 68, 49, 2218, 149, 38, 51, 148, 137, 98, 297, 274, 39, 40, 29, 30, 197, 594, 139, 100, 61, 394, 201, 122, 43, 28, 73, 106, 789, 402, 31, 32
Offset: 1

Views

Author

Antti Karttunen, Mar 13 2016

Keywords

Links

Crossrefs

Inverse: A269864.
Cf. A250469, A268674, A269360.
Differs from similarly constructed A245605 for the first time at n=21, where a(21)=19, instead of 15.

Formula

a(1) = 1, after which for even n, a(n) = 2*a(A268674(n-1)), for odd n, a(n) = 1 + 2*a(A268674(n)-1).

A269360 Permutation of even numbers: a(n) = 1 + A250469(n).

Original entry on oeis.org

2, 4, 6, 10, 8, 16, 12, 22, 26, 28, 14, 34, 18, 40, 36, 46, 20, 52, 24, 58, 56, 64, 30, 70, 50, 76, 66, 82, 32, 88, 38, 94, 86, 100, 78, 106, 42, 112, 96, 118, 44, 124, 48, 130, 116, 136, 54, 142, 122, 148, 126, 154, 60, 160, 92, 166, 146, 172, 62, 178, 68, 184, 156, 190, 120, 196, 72, 202, 176, 208, 74, 214, 80, 220, 186, 226, 144
Offset: 1

Views

Author

Antti Karttunen, Mar 13 2016

Keywords

Links

Crossrefs

Cf. A253886, A250469, A243501.
Cf. also A269863, A269864.

Programs

  • Mathematica
    (* 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[n_] := b[n] + 1;
Array[a, 100] (* Jean-François Alcover, Mar 14 2016 *)
  • Scheme
    (define (A269360 n) (+ 1 (A250469 n)))

Formula

a(n) = 1 + A250469(n).
a(n) = 2 + A253886(n-1).

A269359 Self-inverse permutation of natural numbers: a(1)=1, a(A269360(n)) = A250469(1+a(n)), a(A250469(1+n)) = A269360(a(n)).

Original entry on oeis.org

1, 3, 2, 9, 6, 5, 26, 11, 4, 27, 8, 65, 66, 25, 16, 15, 120, 71, 36, 169, 76, 33, 74, 41, 14, 7, 10, 81, 86, 185, 206, 215, 22, 195, 50, 19, 330, 515, 196, 75, 24, 337, 186, 49, 46, 45, 348, 247, 44, 35, 358, 213, 116, 353, 290, 143, 106, 507, 536, 295, 1266, 1345, 226, 99, 12, 13, 512, 2321, 220, 123, 18, 1285, 306, 23, 40, 21
Offset: 1

Views

Author

Antti Karttunen, Mar 13 2016

Keywords

Links

Crossrefs

Cf. A250469, A268674, A269360.
Similar or related permutations: A244319, A269863, A269864, A269865, A269866, A269867.

Formula

a(1) = 1, after which for even n, a(n) = A250469(1+a(A268674(n-1))), for odd n, a(n) = A269360(a(A268674(n)-1)).
The declarative form can be expressed in terms of A250469 only:
a(1)=1, a(1+A250469(n)) = A250469(1+a(n)), a(A250469(1+n)) = 1+A250469(a(n)).
Showing 1-4 of 4 results.

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