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 1-7 of 7 results.

A210606 Length of the n-th edge of an L-toothpick structure which gives Recamán's sequence A005132.

Original entry on oeis.org

1, 3, 5, 3, 4, 4, 5, 11, 13, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17
Offset: 1

Views

Author

Omar E. Pol, Mar 24 2012

Keywords

Comments

Consider a toothpick structure formed by L-toothpicks connected by their endpoints. The endpoints of the L-toothpicks are placed on the main diagonal of the first quadrant. At stage 1 we place an L-toothpick with one of its endpoints on the origin. At stage n we place an L-toothpick of size n. The L-toothpicks are placed alternately, on one or another sector of the first quadrant, trying to make the structure have an exposed endpoint closest to the origin. The total length of all L-toothpicks after the n-th stage is A002378(n). The value of x and y of the endpoint of the structure after the n-th stage is equal to the n-th term of Recamán's sequence A005132(n). Note that we can get other illustrations of initial terms of Recamán's sequence by replacing each L-toothpick by a Q-toothpick or by a semicircumference. This structure is also one of the three views of the three-dimensional model for Recamán's sequence. For more information about L-toothpicks and Q-toothpicks, see A172310 and A187210.

Examples

			The summands are the size of the L-toothpicks:
a(1) = 1.
a(2) = 1 + 2 = 3.
a(3) = 2 + 3 = 5.
a(4) = 3.
a(5) = 4.
a(6) = 4.
a(7) = 5.
a(8) = 5 + 6 = 11.
a(9) = 6 + 7 = 13.
a(10) = 7.

Links

Crossrefs

First differences of A210607.
Cf. A005132, A064289, A119632, A139250, A160356, A160357, A171175, A171178, A172310, A187210, A210604, A210605, A210608-A210613.

A210607 Vertex number of an L-toothpick structure which give Recamán's sequence A005132.

Original entry on oeis.org

0, 1, 4, 9, 12, 16, 20, 25, 36
Offset: 1

Views

Author

Omar E. Pol, Mar 24 2012

Keywords

Comments

For more information see A210606.

Links

Crossrefs

First differences give A210606.
A002378, A005132, A119632, A139250, A160356, A171175, A171178, A172310, A187210, A210607-A210613.

A210612 Number of nonnegative integers smaller than the largest number of Recamán's A005132 after the n-th stage that are not yet in Recamán's sequence at that stage.

Original entry on oeis.org

0, 1, 3, 2, 2, 7, 13, 12, 12, 11, 11, 10, 10, 9, 9, 8, 8, 25, 43, 42, 42, 41, 40, 40, 39, 39, 38, 37, 36, 35, 34, 33, 48, 81, 80, 80, 79, 78, 78, 77, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 95, 161, 160, 160
Offset: 1

Views

Author

Omar E. Pol, Mar 25 2012

Keywords

Comments

Row length of row n of A210762.
Number of grid points that are not covered after n-th stage on the axis of the structure mentioned in A210606 which is a model for the visualization of Recamán's sequence.

Links

Crossrefs

Cf. A005132, A064291, A210606-A210611, A210613, A210762.

Programs

Extensions

a(20) and beyond by R. J. Mathar, Apr 01 2012

A210608 Number of intersections after n-th stage in the structure mentioned in A210606 using semicircumferences and counting the superposed intersections several times.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 14, 22, 28, 36, 43
Offset: 1

Views

Author

Omar E. Pol, Mar 25 2012

Keywords

Comments

The structure mentioned in A210606 is a model for the visualization of Recamán's sequence A005132.
First differs from A210609 at a(24).

Links

Crossrefs

Cf. A005132, A064289, A119632, A160356, A160357, A171175, A171178, A210606, A210607, A210609-A210613.

A210609 Number of intersections after n-th stage in the structure mentioned in A210606 using semicircumferences and counting the superposed intersections only once.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 14, 21, 27
Offset: 1

Views

Author

Omar E. Pol, Mar 25 2012

Keywords

Comments

The structure mentioned in A210606 is a model for the visualization of Recamán's sequence A005132.
First differs from A210608 at a(24).

Links

Crossrefs

Cf. A005132, A064289, A119632, A160356, A160357, A171175, A171178, A210606, A210607, A210608, A210610-A210613.

A210610 Number of semicircumferences in the n-th spiral of the structure mentioned in A210606.

Original entry on oeis.org

3, 11, 4, 10, 4, 28, 10, 24, 8, 2, 4, 9, 4, 2, 36, 12, 4, 2, 3, 28, 10, 52, 18, 32, 12, 15, 38, 14, 32, 12, 44, 16, 148, 50, 7, 22, 8, 3, 4, 2, 70, 24, 114, 42, 200, 68, 6, 2, 13
Offset: 1

Views

Author

Omar E. Pol, Mar 25 2012

Keywords

Comments

The structure mentioned in A210606 is a model for the visualization of Recamán's sequence A005132.

Links

Crossrefs

Numbers > 1 in A119632.
Cf. A005132, A064289, A160356, A160357, A171175, A171178, A210606-A210609, A210611-A210613.

A210762 Triangle read by rows in which row n lists the positive integers smaller than the currently largest number in Recamán's sequence A005132 after the n-th stage, but not yet present in Recamán's sequence.

Original entry on oeis.org

2, 2, 4, 5, 4, 5, 4, 5, 4, 5, 8, 9, 10, 11, 12, 4, 5, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 4, 5, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 4, 5, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 4, 5, 8, 9, 10, 14, 15, 16, 17, 18, 19, 4, 5, 8, 9, 10, 14, 15, 16, 17
Offset: 2

Views

Author

Omar E. Pol, Mar 25 2012

Keywords

Comments

The number of positive integers in row n is A210612(n).

Examples

			Written as an irregular triangle:
2;
2, 4, 5;
4, 5;
4, 5;
4, 5, 8, 9, 10, 11, 12;
4, 5, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19;
4, 5, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19;
4, 5, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19;
4, 5, 8, 9, 10, 14, 15, 16, 17, 18, 19;

Links

Crossrefs

Cf. A005132, A210606-A210613.

Programs

  • Maple
    A210762 := proc(n)
        local L,maxa ;
        rec := [seq(A005132(j),j=0..n)] ;
        maxa := max(op(rec)) ;
        L := [] ;
        for i from 0 to maxa do
                if not member(i,rec) then
                        L := [op(L),i] ;
                end if;
        end do;
        if nops(L) = 0 then
                return [0] ;
        end if;
        L ;
end proc:
seq(op(A210762(n)),n=1..11) ; # R. J. Mathar, Apr 01 2012
Showing 1-7 of 7 results.

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