A139254 -id:A139254

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A139252

Number of segments needed to draw the toothpick structure of A139250 as it is after n stages.

+10
17

0, 1, 3, 5, 7, 11, 15, 17, 19, 23, 27, 31, 39, 51, 59, 61, 63, 67, 71, 75, 83, 95, 103, 107, 115, 127, 139, 155, 183, 215, 231, 233, 235, 239, 243, 247, 255, 267, 275, 279, 287, 299, 311, 327, 355, 387, 403, 407, 415 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,3`
	COMMENTS	`Contribution from Omar E. Pol, Sep 16 2012 (Start):` `It appears that A147614(n)/a(n) converge to 4.` `It appears that A139250(n)/a(n) converge to 3.` `It appears that A160124(n)/a(n) converge to 2.` `(End)`
	LINKS	`Nathaniel Johnston, Table of n, a(n) for n = 0..256` `David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]` `Nathaniel Johnston, C script for computing table of terms` `N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS`
	EXAMPLE	`For n = 3, after three stages the toothpick structure of A139250 contains seven toothpicks (A139250(3) = 7), however the toothpick structure can be essentially represented by five segments, so a(3) = 5. - Omar E. Pol, Sep 16 2012`
	CROSSREFS	`Cf. A139250, A139251, A139253, A147614, A160124, A139254, A139255, A160128.`
	KEYWORD	`nonn`
	AUTHOR	`Omar E. Pol, May 17 2008`
	EXTENSIONS	`Terms after a(28) from Nathaniel Johnston, Mar 29 2011`
	STATUS	`approved`

A139560

Number of new segments added to the toothpick structure drawing at the n-th step (extensions of earlier segments are not considered).

+10
6

1, 2, 2, 2, 4, 4, 2, 2, 4, 4, 4, 8, 12, 8, 2, 2, 4, 4, 4, 8, 12, 8, 4, 8, 12, 12, 16, 28, 32, 16, 2, 2, 4, 4, 4, 8, 12, 8, 4, 8, 12, 12, 16, 28, 32, 16, 4, 8, 12, 12, 16, 28, 32, 20, 16, 28, 36, 40, 60, 88, 80, 32 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	COMMENTS	`First differences of A139252.`
	LINKS	`Table of n, a(n) for n=1..62.` `David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]` `N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS`
	FORMULA	`a(n)=A139252(n)-A139252(n-1).`
	CROSSREFS	`Cf. A139250, A139251, A139252, A139253, A139254, A139559.`
	KEYWORD	`nonn`
	AUTHOR	`Omar E. Pol, May 17 2008`
	EXTENSIONS	`Terms after a(28) from Nathaniel Johnston, Mar 29 2011`
	STATUS	`approved`

A139255

Complement of toothpick sequence A139250.

+10
1

2, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	LINKS	`Table of n, a(n) for n=1..61.` `David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]` `N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS`
	CROSSREFS	`Cf. A139250, A139251, A139252, A139253, A139254.`
	KEYWORD	`nonn`
	AUTHOR	`Omar E. Pol, May 11 2008, Jan 02 2009`
	STATUS	`approved`

A139559

Primes in A139252 (related to the toothpick structure).

+10
1

3, 5, 7, 11, 17, 19, 23, 31, 59, 61, 67, 71, 83, 103, 107, 127, 139, 233, 239, 311, 439, 883, 919, 971, 983, 1039, 1087, 1091, 1123, 1399, 1487, 1567, 1747, 1811, 1999, 2131, 2383, 2467, 2927, 3391, 3583, 3659, 3671, 3691 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	LINKS	`Table of n, a(n) for n=1..44.` `David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]` `N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS`
	CROSSREFS	`Cf. A139250, A139251, A139252, A139253, A139254.`
	KEYWORD	`nonn`
	AUTHOR	`Omar E. Pol, May 17 2008`
	EXTENSIONS	`Terms after a(17) from Nathaniel Johnston, Mar 29 2011`
	STATUS	`approved`

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