A139252 -id:A139252 - cp's OEIS frontend

A139254 Primes that are not toothpick primes.

2, 5, 13, 17, 19, 29, 31, 37, 41, 53, 59, 61, 71, 73, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191

Offset: 1

Omar E. Pol, May 11 2008

nonn

Primes that are not members of A139253.

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

Cf. A000040, A139250, A139251, A139252, A139253.

A152768 Records in A139251.

Original entry on oeis.org

1, 2, 4, 8, 12, 16, 28, 32, 36, 40, 60, 88, 92, 112, 140, 208, 256, 260, 296, 364, 488, 672, 704, 708, 744, 956, 1216, 1648, 2048, 2052, 2096, 2108, 2396, 3128, 4080, 5344, 5952, 5956, 6000, 6300, 7920, 10336, 13504, 16640, 16644, 16688, 16696, 16988, 17100, 18612, 20040

Offset: 1

Omar E. Pol, Dec 15 2008, Dec 20 2008

nonn

Excluding the initial 1 and 2, this sequence also gives the records in A147646. - Nathaniel Johnston, Apr 10 2011

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

Cf. A139251, A139252, A139560. Toothpick sequence: A139250.

Cf. A052184.

a(18) - a(51) from Nathaniel Johnston, Apr 10 2011

A152973 Records in A152968.

Original entry on oeis.org

1, 2, 4, 6, 8, 14, 16, 18, 20, 30, 44, 46, 56, 70, 104, 128, 130, 148, 182, 244, 336, 352, 354, 372, 478, 608, 824, 1024, 1026, 1048, 1054, 1198, 1564, 2040, 2672, 2976, 2978, 3000, 3150, 3960, 5168, 6752, 8320, 8322, 8344, 8348, 8494, 8550, 9306

Offset: 1

Omar E. Pol, Dec 16 2008

nonn

Excluding the initial 1, this sequence also gives the records in A151688. - Nathaniel Johnston, Apr 10 2011

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

Toothpick structure: A139250.
Cf. A139251, A139252, A152968.
Cf. A152978.

More terms from Omar E. Pol, Dec 20 2008

a(17)-a(49) from Nathaniel Johnston, Apr 10 2011

A139255 Complement of toothpick sequence A139250.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, May 11 2008, Jan 02 2009

nonn

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

Cf. A139250, A139251, A139252, A139253, A139254.

A210985 Number of segments needed to draw the toothpick structure of A139250 as it is after 2^n stages.

Original entry on oeis.org

1, 3, 7, 19, 63, 235, 919, 3651, 14575

Offset: 0

Omar E. Pol, Sep 11 2012

It appears that this is also the partial sums of A039301.

It appears that this is also 1 together with A160128.

			For n = 3, after 2^3 stages the toothpick structure of A139250 contains 43 toothpicks (A139250(2^3) = 43). However the toothpick structure can be essentially represented by 19 segments (A139252(2^3) = 19), so a(3) = 19.

David Applegate, The movie version
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Cf. A007583, A039301, A139250, A139252, A147614, A160128.

a(n) = A139252(2^n).

A168115 a(n) = A139560(n+1)/2.

Original entry on oeis.org

1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 4, 6, 4, 1, 1, 2, 2, 2, 4, 6, 4, 2, 4, 6, 6, 8, 14, 16, 8, 1, 1, 2, 2, 2, 4, 6, 4, 2, 4, 6, 6, 8, 14, 16, 8, 2, 4, 6, 6, 8, 14, 16, 10, 8, 14, 18, 20, 30, 44, 40, 16, 1, 1, 2, 2, 2, 4, 6, 4, 2, 4, 6, 6, 8, 14, 16

Offset: 1

Omar E. Pol, Dec 09 2009

nonn

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

Cf. A139250, A139252, A139560.

Terms after a(27) from Nathaniel Johnston, Mar 29 2011

cp's OEIS Frontend

A139254 Primes that are not toothpick primes.

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A152768 Records in A139251.

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A152973 Records in A152968.

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A139255 Complement of toothpick sequence A139250.

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A210985 Number of segments needed to draw the toothpick structure of A139250 as it is after 2^n stages.

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A168115 a(n) = A139560(n+1)/2.

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