On-Line Encyclopedia of
Unknown or Ambiguous
Integer Sequences
Index :
B010000....Divisor
B020000....Graph theory
B030000....K-sequence
B040000....Others
ID Number : B010001
Sequence :
6943520030720, 5386209454080, 6389772480000, 7665533854902, 575659229184, 5657834203560, 6382469882880, 7938550287360, 9055131471360, 9256155068160, 11798498589696, 12316979136000, 13937317954560, 18314063179776, 18071888486400, 20136798781440, 18850467643392, 16492422758400, 15699547839573, 6635615891520, 7400619883008, 6494644316160, 8009835724800, 9317732578770, 7847237806128
Name : 1/4-sigma or 1/4-aliquot sequence. It is defined as follows.
b(n)=1/4*sigma(b(n-1))
Comment : It is a periodic sequence whose period is 25.
so, it is also called a 1/4-sigma sosiable number.
Keyword : periodic
Offset : 6943520030720
Author : Yasutoshi
ID Number : B020001
Sequence : oo, oo, 7, 6, 5, 5, 5, 5, 5, 5
"oo" means infinity
Name : Chromatic number of Near_{2,n}(G).
Where G is a planar graph.
A mapping Near_{2,n} : G -> G' is defined as follows.
If we add all edges between two vertices which are (2,n) on G, then G becomes Near_{2,n}(G).
Definition of (2,n) :
n edges of length two exist between different two vertices.
Comment : b(n)=5 , 4<n
Keyword :
Offset : 1
Author : Yasutoshi
ID Number : B020002
Sequence : oo, oo, 12, 10, 9, 9, 7, 7, 7, 7
"oo" means infinity
Name : Chromatic number of Near_{2,n}(H).
Where H is a turus graph.
A mapping Near_{2,n} : H -> H' is defined as follows.
If we add all edges between two vertices which are (2,n) on H, then H
becomes Near_{2,n}(H).
Definition of (2,n) :
n edges of length two exist between different two vertices.
Comment : b(n)=7 , 6<n
These numbers are lower bound.
Keyword : unknown
Offset : 1
Author : Yasutoshi
ID Number B030001
Sequence : 2443670343, 2443841401, 2444012471, 2444183553, 2444354647, 2444525753, 2444696871, 2444868001, 2445039143, 2445210297, 2445381463, 2445552641, 2445723831, 2445895033, 2446066247, 2446237473, 2446408711, 2446579961, 2446751223, 2446922497, 2447093783, 2447265081, 2447436391, 2447607713, 2447779047, 2447950393
Name : K-Sequence
b(n-+1)=[A*b(n-1)+B]/p^r
Where [m] is integer part of n. A,B are real numbers. p^r is the highest power of p dividing [A*a(n-1)+B]
p=2, A=2.00014, B=3.0
Comment : The first 68 terms are represented as follows :
x(n) = 6*n^2+171040*n+2443499297
Why does K-Sequence generate such a polynomial sequence?
After 68-th term, it becomes random like and it has many linear parts.
Period = 73667
Keyword : Periodic, Extremely strange
Offset : 2443670343
Author : Yasutoshi
ID Number B030002
Sequence : 2015985557869547951, 2016116596930809473, 2016247644509609977, 2016378700606503103, 2016509765222042527, 2016640838356781961, 2016771920011275153, 2016903010186075887, 2016116596930809473, 2016247644509609977
Name : K-Sequence
b(n-+1)=[A*b(n-1)+B]/p^r
Where [m] is integer part of n. A,B are real numbers. p^r is the highest power of p dividing [A*a(n-1)+B]
p=2, A=2.00013, B=3.2
Comment : The first 8 terms are fourth degree sequence.
After 8-th term, it becomes random like and it has many linear parts.
Period = 6366
Keyword : Periodic, Extremely strange
Offset : 2015985557869547951
Author : Yasutoshi
ID Number B030003
Sequence : 15371, 15373, 15375, 15377, 15379, 15381, 15383, 15385, 30775, 61557, 123125, 246269, 492573, 985213, 1970557, 3941373, 7883261, 15767549, 15768575,
Name : K-Sequence
b(n-+1)=[A*b(n-1)+B]/p^r
Where [m] is integer part of n. A,B are real numbers. p^r is the highest power of p dividing [A*a(n-1)+B]
p=2, A=2.00013, B=3.0
Comment : It is the end part of the first linear subsequence of A029580 which continued to 3008-th term.
Period =1790641
Keyword : Periodic, Extremley strange
Offset : 15371
Author : Yasutoshi