keyword:unkn - cp's OEIS frontend

A131393 Conjectured permutation of the positive integers using Rule 2 with a(1)=1.

1, 2, 4, 3, 6, 10, 8, 5, 11, 7, 12, 19, 14, 22, 16, 9, 18, 28, 20, 31, 21, 33, 24, 13, 26, 40, 27, 42, 30, 15, 32, 48, 34, 17, 35, 54, 38, 58, 39, 60, 37, 59, 41, 64, 44, 23, 47, 25, 50, 76, 52, 79, 53, 81, 56, 29, 61, 90, 62, 92, 63, 94, 57, 91, 55, 88, 49, 84, 51, 87, 46, 83

Offset: 1

Clark Kimberling, Jul 05 2007

Conjecture 1: a( ) is a permutation of the positive integers. Conjecture 2: d( ) is a permutation of the integers. The sequence using Rule 1 ("negative before positive") is A131388.

This sequence was generated using "Rule 2" in a computer program which been lost. The wording of "Rule 2" in the Formula section, although flawed, is retained in case someone can rediscover "Rule 2" and contribute a corrected version. - Clark Kimberling, May 18 2015

			a(2)=1+1, a(3)=a(2)+2, a(4)=a(3)+(-1), a(5)=a(4)+3, a(6)=a(5)+4.
The first term that differs from A131388 is a(28)=42.

Table of n, a(n) for n = 1..72

Cf. A131388, A131389, A131390, A131391, A131392, A131394, A131395, A131396, A131397.

The following version of "Rule 2" is defective; see Comments. - Clark Kimberling, May 18 2015

Rule 2 ("positive before negative"): define sequences d( ) and a( ) as follows: d(1)=0, a(1)=1 and for n>=2, d(n) is the least positive integer d such that a(n-1)+d is not among a(1), a(2),...,a(n-1), or, if no such d exists, then d(n) is the greatest negative integer d such that a(n-1)+d is not among a(1), a(2),...,a(n-1). Then a(n)=a(n-1)+d.

A131394 Conjectured permutation of the integers using Rule 2 with A131393(1)=1.

Original entry on oeis.org

0, 1, 2, -1, 3, 4, -2, -3, 6, -4, 5, 7, -5, 8, -6, -7, 9, 10, -8, 11, -10, 12, -9, -11, 13, 14, -13, 15, -12, -15, 17, 16, -14, -17, 18, 19, -16, 20, -19, 21, -23, 22, -18, 23, -20, -21, 24, -22, 25, 26, -24, 27, -26, 28, -25, -27, 32, 29, -28, 30, -29, 31, -37, 34, -36, 33, -39, 35, -33

Offset: 1

Clark Kimberling, Jul 05 2007

Rule 2 is given at A131393. Conjecture: A131394 is a permutation of the integers.

			See A131393.

Table of n, a(n) for n = 1..69

Cf. A131388, A131389, A131390, A131391, A131392, A131393, A131395, A131396, A131397.

This is the sequence d( ) in the formula for A131393.

A002875 Sorting numbers (see Motzkin article for details).

Original entry on oeis.org

1, 2, 4, 24, 128, 880, 7440

Offset: 0

N. J. A. Sloane

How is the sequence defined (see the links in A000262)? Also more terms would be welcome.

Based on the Motzkin article, where this sequence appears in the last row of the table on p. 173, one would expect that this sequence is the same as A294202. However, they seem to be unrelated. So the true definition of this sequence is a mystery. - Andrew Howroyd and Andrey Zabolotskiy, Oct 25 2017

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Victor Meally, Comparison of several sequences given in Motzkin's paper "Sorting numbers for cylinders...", letter to N. J. A. Sloane, N. D.
T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]
OEIS Wiki, Sorting numbers
Index entries for sequences related to sorting

Cf. A000262, A001861, A002872, A002873, A002874, A036073, A294201, A294202.

A007458 Order of group of n X n X n Rubik cube.

Original entry on oeis.org

1, 24, 1058158080, 173008013097959424000

Offset: 1

N. J. A. Sloane

It would be nice to have a more precise definition of this sequence! - N. J. A. Sloane, Feb 28 2003.

a(2) = A054434(1)*24, a(3) = A054434(2)*12, a(4) = A054434(3)*4. - Andrey Zabolotskiy, Jun 26 2016

J. H. Conway, personal communication.
Rowley, Chris, The group of the Hungarian magic cube, in Algebraic structures and applications (Nedlands, 1980), pp. 33-43, Lecture Notes in Pure and Appl. Math., 74, Dekker, New York, 1982.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Xavier Servantie, All about Rubik's cube
Index entries for sequences related to groups

See A054434, A074914, A075152 for other versions.

A035403 Related to Rogers-Ramanujan Identities.

Original entry on oeis.org

4, 8, 12, 32, 37, 45, 68, 74, 80, 85, 97, 197, 202, 215, 218, 225, 239, 243, 253, 272, 374, 380, 387, 392, 420, 424, 428, 438, 463, 470, 484

Offset: 1

Olivier Gérard

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
Contact author at address below [ Note: this form of description is not acceptable! - N. J. A. Sloane ]

Cf. A003114, A035401, A035402, A035404, A035405.

A103752 Erroneous version of: Primes from merging of 10 successive digits in decimal expansion of the Golden Ratio: (1+sqrt(5))/2.

Original entry on oeis.org

1885371871, 1467894749, 1927385857, 1044320141, 1696498873, 1208796539, 1404814871, 1388362561, 1165339067, 1653392113, 1112115161, 1678526879, 1021710497, 1225884823, 1092051469, 2035361123, 1439829827, 1122708877

Offset: 0

Andrew G. West (WestA(AT)wlu.edu), Mar 29 2005

What is this sequence? The correct version is A198177. - Bruno Berselli, May 01 2013

All terms are less than 2^31, this seems to indicate that the author made calculations with signed 32-bit integers, similar to A105383. But in contrast to that sequence, none of the terms here is obtained by using this procedure (taking mod 2^32 and selecting primes between 10^9 and 2^31). Does the present sequence rather relate to a different constant? - M. F. Hasler, Nov 01 2014

Simon Plouffe, Expansion of the Golden Ratio done to 20,000 digits as part of project Gutenberg.
Eric Weisstein's World of Mathematics, Golden Ratio.

Cf. A198177.

Broken URL to Project Gutenberg replaced by Georg Fischer, Jan 03 2009

A052281 Number of 4 X 4 symmetric stochastic matrices under row and column permutations.

Original entry on oeis.org

1, 1, 3, 6, 16, 29, 62, 107, 195, 320, 522, 804, 1234, 1804, 2626, 3700, 5155, 7038

Offset: 0

Vladeta Jovovic, Feb 06 2000

This sequence appears to be an erroneous version of A333886.

			There are 6 nonisomorphic symmetric 4 X 4 matrices with row and column sums 3:
[0 0 0 3] [0 0 1 2] [0 0 1 2] [0 0 1 2] [0 0 1 2] [0 1 1 1]
[0 0 3 0] [0 0 2 1] [0 1 1 1] [0 1 2 0] [0 2 1 0] [1 0 1 1]
[0 3 0 0] [1 2 0 0] [1 1 1 0] [1 2 0 0] [1 1 0 1] [1 1 0 1]
[3 0 0 0] [2 1 0 0] [2 1 0 0] [2 0 0 1] [2 0 1 0] [1 1 1 0]
But, A333886 gives 6 other cases.

Cf. A053493, A001496, A052280, A052282.

A115603 My teacher gave this as a "riddle".

Original entry on oeis.org

1, 10, 14, 30

Offset: 0

Len Burman (lburman6(AT)comcast.net), Mar 13 2006

Possibly a version of A116955? - Arkadiusz Wesolowski, Mar 16 2011

A104101 The Lost Numbers.

Original entry on oeis.org

4, 8, 15, 16, 23, 42

Offset: 0

Marcus Dicander, Mar 04 2005

These numbers were central to the plot of the TV-series "Lost", episodes 18 and 201.
Another number in the sequence, perhaps the next one, is 540: the number of days which the team of two people who are addressed by the orientation film are to stay at station 3. 4+8+15+16+23+42 = 108 and 108 * 5 = 540. - Joshua Walton (joshuawalton(AT)hotmail.com), May 05 2006
According to the show, 108 is not officially a part of the sequence, it just happens to be the sum of those numbers. - Ville Saalo (vsaalo(AT)iki.fi), Nov 19 2006
For n = 0,1,2,3,4,5 (1/120)(42n^5 - 305n^4 + 1100n^3 - 895n^2 + 1018n + 480) gives 4,12,35,89,213,511 -- the binomial transform of 4,8,15,16,23,42. The sequence continues 1194,2622,5346,10150,18093.... The polynomial (1/120)(42x^5 - 305x^4 + 1100x^3 - 895x^2 + 1018x + 480) is the "Shaw-Basho polynomial". - Ross La Haye, Feb 26 2007

Marcus Dicander, The Lost Numbers: 4 8 15 16 23 42
Lostpedia contributors, "The Numbers", Lostpedia
Doug Shaw, The Lost Sequence
Wikipedia, Mythology of Lost

Cf. A122115, A130826.

It is easy to fit formulas to the first six terms, in a million different ways, but none of them are of any interest (the seventh term can be chosen to be any number you wish). - N. J. A. Sloane, Oct 22 2017

A007762 Number of domino tilings of a certain region.

Original entry on oeis.org

1, 8, 120, 2288, 49680, 1170968, 29206632, 759265760, 20371816992, 560386232744

Offset: 1

James Propp

Jon Maiga, Computer-generated formulas for A007762, Sequence Machine.
Index entries for sequences related to dominoes

a(n) = A006318(n-1) * A104550(n) for all known terms [discovered by Sequence Machine]. - Andrey Zabolotskiy, Oct 12 2021

cp's OEIS Frontend

A131393 Conjectured permutation of the positive integers using Rule 2 with a(1)=1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A131394 Conjectured permutation of the integers using Rule 2 with A131393(1)=1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A002875 Sorting numbers (see Motzkin article for details).

Views

Author

Keywords

Comments

References

Links

Crossrefs

A007458 Order of group of n X n X n Rubik cube.

Views

Author

Keywords

Comments

References

Links

Crossrefs

A035403 Related to Rogers-Ramanujan Identities.

Views

Author

Keywords

References

Crossrefs

A103752 Erroneous version of: Primes from merging of 10 successive digits in decimal expansion of the Golden Ratio: (1+sqrt(5))/2.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A052281 Number of 4 X 4 symmetric stochastic matrices under row and column permutations.

Views

Author

Keywords

Comments

Examples

Crossrefs

A115603 My teacher gave this as a "riddle".

Views

Author

Keywords

Comments

A104101 The Lost Numbers.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A007762 Number of domino tilings of a certain region.

Views

Author

Keywords

Links

Formula