A210604 -id:A210604 - cp's OEIS frontend

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

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

Omar E. Pol, Mar 24 2012

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.

			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.

First differences of A210607.

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

A210605 Bisection of Recamán's sequence A005132.

Original entry on oeis.org

1, 6, 7, 20, 21, 22, 23, 24, 25, 62, 63, 18, 17, 16, 15, 14, 79, 78, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 224, 225, 226, 227, 228, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 265, 264, 263, 262, 261, 40, 265, 494, 495, 258, 259

Offset: 1

Omar E. Pol, Mar 23 2012

Also length of the vertical edges of a rectangular polyspiral path. For the horizontal edges see A210604. The mentioned polyspiral path is one of the three views of a rectangular polyhelix which is a three-dimensional graphical representation of Recamán's sequence A005132.

			1) Written as an irregular array in which each row lists consecutive numbers in ascending order or in descending order:
1;
6,7;
20,21,22,23,24,25;
62,63;
18,17,16,15,14;
79,78,77;
78,79,80,81,82,83,84,85,86,87,88,89,90,91;
...
2) Written as an irregular array in which each row lists consecutive numbers in ascending order, in descending order or in descending-ascending order:
1;
6,7;
20,21,22,23,24,25;
62,63;
18,17,16,15,14;
79,78,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91;
...

Index entries for sequences related to Recamán's sequence

Cf. A005132, A065056, A171175, A171178, A210604-A210607.

cp's OEIS Frontend

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

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