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.

Previous Showing 11-18 of 18 results.

A065287 Infinite binary tree inspired permutation of N: 1 -> 3, 11ab..yz -> 11ab..yz1, 10ab..y0 -> 10ab..y, 10ab..y1 -> 11ab..y0.

Original entry on oeis.org

3, 1, 7, 2, 6, 13, 15, 4, 12, 5, 14, 25, 27, 29, 31, 8, 24, 9, 26, 10, 28, 11, 30, 49, 51, 53, 55, 57, 59, 61, 63, 16, 48, 17, 50, 18, 52, 19, 54, 20, 56, 21, 58, 22, 60, 23, 62, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 32, 96, 33, 98
Offset: 1

Views

Author

Antti Karttunen, Oct 28 2001

Keywords

Comments

On the right side every node replaces its right child, on the left side the left children replace their parents and the right children are transferred to the same offset - 1 at the right side (becoming left children). See comment at A065263.

Links

Crossrefs

A057114, A065263, A065269, A065275, A065281. Inverse: A065288, conjugated with A059893: A065289 and the inverse of that: A065290.

Programs

  • Maple
    RightChildTransferred_1 := proc(n) local k; if(1 = n) then RETURN(3); fi; k := floor_log_2(n)-1; if(3 = floor(n/(2^k))) then RETURN((2*n)+1); fi; if(0 = (n mod 2)) then RETURN(n/2); fi; RETURN(n + (2^k) - 1); end;

A065627 Permutation of N induced by rotating the node 2 right in the infinite planar binary tree. The second row of A065625. Inverse of A065628.

Original entry on oeis.org

1, 5, 3, 2, 11, 6, 7, 4, 10, 22, 23, 12, 13, 14, 15, 8, 9, 20, 21, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 40, 41, 42, 43, 88, 89, 90, 91, 92, 93, 94, 95, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 32, 33, 34, 35, 36, 37, 38, 39, 80, 81, 82, 83, 84, 85, 86, 87, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186
Offset: 1

Views

Author

Antti Karttunen, Nov 08 2001

Keywords

Links

Crossrefs

A065627[n] = A057114[A065631[A057115[n]]]. Stabilizes the set A004760.

Programs

  • Maple
    [seq(RotateNodeRight(2,j),j=1..120)];

A065631 Permutation of N induced by rotating the node 4 right in the infinite planar binary tree. The fourth row of A065625. Inverse of A065632.

Original entry on oeis.org

1, 2, 3, 9, 5, 6, 7, 4, 19, 10, 11, 12, 13, 14, 15, 8, 18, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 36, 37, 76, 77, 78, 79, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 32, 33, 34, 35, 72, 73, 74, 75, 152, 153, 154, 155, 156, 157, 158, 159, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91
Offset: 1

Views

Author

Antti Karttunen, Nov 08 2001

Keywords

Links

Crossrefs

A065631[n] = A057115[A065627[A057114[n]]]

Programs

  • Maple
    [seq(RotateNodeRight(4,j),j=1..120)];

A065250 Permutation of N induced by the order-preserving permutation of the positive rational numbers (x -> 2x), positions in Stern-Brocot tree.

Original entry on oeis.org

3, 1, 15, 5, 12, 7, 63, 2, 23, 48, 6, 29, 60, 31, 255, 9, 20, 11, 95, 192, 24, 51, 26, 14, 119, 240, 30, 125, 252, 127, 1023, 4, 39, 80, 10, 45, 92, 47, 383, 768, 96, 195, 98, 25, 207, 104, 13, 57, 116, 59, 479, 960, 120, 243, 122, 62, 503, 1008, 126, 509, 1020, 511
Offset: 1

Views

Author

Antti Karttunen, Oct 25 2001

Keywords

Links

Crossrefs

Cf. A057114, A065251. Inverse permutation A065249.

Programs

  • Maple
    [seq(A065250(j),j=1..120)]; A065250 := n -> frac2position_in_whole_SB_tree((SternBrocotTreeNum(n)/SternBrocotTreeDen(n))*2);

A207790 Permutation of positive numbers. See comments.

Original entry on oeis.org

1, 2, 4, 3, 8, 5, 6, 7, 16, 11, 9, 13, 12, 17, 10, 19, 32, 23, 14, 29, 18, 31, 15, 37, 24, 41, 21, 43, 20, 47, 22, 53, 64, 59, 25, 61, 27, 67, 26, 71, 36, 73, 33, 79, 28, 83, 34, 89, 48, 97, 35, 101, 30, 103, 38, 107, 40, 109, 39, 113, 42, 127, 46, 131, 128, 137, 49, 139, 44, 149, 51, 151
Offset: 1

Views

Author

Vladimir Shevelev and Peter J. C. Moses, Feb 20 2012

Keywords

Comments

a(1)=1; on places 2,4,6,8,... we put primes (A000040); on places 3,7,11,15,... we put products of two primes (A001358); on places 5,13,21,29,... we put products of three primes (A014612); on places 9,25,41,57,... we put products of four primes (A014613); on places 17,49,81,... we put products of five primes (A014614); etc.
Primes with the index not exceeding n have density 1/2, semiprimes have density 1/4, etc.
By our system, here and in A207800, A207801, A207802 we used the order: a(1)=1; the first appearance of a new kind of numbers in places of the form 2^k+1, k=0,1,2,..., with period of the appearance 2^{k+1}.

Links

Crossrefs

Cf. A057114.

Programs

  • Mathematica
    mx = 72; a = Array[1 &, mx]; cnt = mx - 1; offs = Table[2^(i - 1) + 1, {i, 1, mx}]; n = 1; While[cnt > 0, n++; idx = PrimeOmega[n]; pos = offs[[idx]]; If[pos > mx, Continue[]]; offs[[idx]] += 2^idx; a[[pos]] = n; cnt--]; a (* Ivan Neretin, May 06 2015 *)

Formula

For n>1, a(n) = A078840(A249725(n-1)). - Ivan Neretin, Apr 30 2016

A065637 Permutation of N induced by rotating the node 7 right in the infinite planar binary tree. The seventh row of A065625. Inverse of A065638.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 15, 8, 9, 10, 11, 12, 13, 7, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 14, 30, 62, 63, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 28, 29, 60, 61, 124, 125, 126, 127, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92
Offset: 1

Views

Author

Antti Karttunen, Nov 08 2001

Keywords

Links

Crossrefs

A065637[n] = A057114[A065629[A057115[n]]]

Programs

  • Maple
    [seq(RotateNodeRight(7,j),j=1..120)];

A065639 Permutation of N induced by rotating the node 8 right in the infinite planar binary tree. The eighth row of A065625. Inverse of A065640.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 17, 9, 10, 11, 12, 13, 14, 15, 8, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 34, 70, 71, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 32, 33, 68, 69, 140, 141, 142, 143, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92
Offset: 1

Views

Author

Antti Karttunen, Nov 08 2001

Keywords

Links

Crossrefs

A065639[n] = A057115[A065631[A057114[n]]] = A057115[A057115[A065627[A057114[A057114[n]]]]]

Programs

  • Maple
    [seq(RotateNodeRight(8,j),j=1..120)];

A065640 Permutation of N induced by rotating the node 8 left in the infinite planar binary tree. The eighth row of A065626. Inverse of A065639.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 16, 9, 10, 11, 12, 13, 14, 15, 32, 8, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 64, 65, 33, 17, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 128, 129, 130, 131, 66, 67, 34, 35, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92
Offset: 1

Views

Author

Antti Karttunen, Nov 08 2001

Keywords

Links

Crossrefs

A065640[n] = A057115[A065632[A057114[n]]] = A057115[A057115[A065628[A057114[A057114[n]]]]]

Programs

  • Maple
    [seq(RotateNodeLeft(8,j),j=1..120)];
Previous Showing 11-18 of 18 results.

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