technical question for oeis-entries
Gottfried Helms
Annette.Warlich at t-online.de
Sat Aug 27 08:15:02 CEST 2005
Seqfans -
just came across a sequence which I submitted earlier, and I would like to
format the comments and examples a bit better, at least with linebreaks,
but don't want to experiment with and possibly spoil actual contents of the OEIS.
Example:
ID Number: A096773
URL: http://www.research.att.com/projects/OEIS?Anum=A096773
Sequence: 0,3,1,13,5,53,21,213,85,853,341,3413,1365,13653,5461,54613,
21845,218453,87381,873813,349525,3495253,1398101,13981013,
5592405,55924053,22369621,223696213,89478485,894784853,
357913941,3579139413,1431655765
Name: a(n+2) = 4*a(n) + 1; a(1)=0, a(2) = 3.
Comments: Remainders for classes m of integers n (mod 2^(m+1)) which divide the
integers in 2 groups after one Collatz (3x+1)-transformation.
With one 3x+1-transformation T(x;p) := x'= (3x+1)/2^p all numbers of
the form x = i*2^N +a(N) -> x' = i*6 + 1 for odd N>2, -> x' = i*6 + 5
for even N. x = 4*i + 3 -> x' = 6*i + 5, x = 8*i + 1 -> x' = 6*i + 1, x =16*i +13
-> x' = 6*i + 5, x = 32*i + 1 -> x' = 6*i + 1, x =64*i +53 -> x' = 6*i + 5, x
=128*i + 1 -> x' = 6*i + 1, with i a free parameter >=0
Formula: a(2m) = (5*2^(2m-1) - 1)/3, a(2m-1) = (2^(2m-2)-1)/3.
Example: a(1) = (2^0-1)/3 = 0, a(2) = (5*2^1 - 1) / 3 = 3, a(3) = (2^2-1)/3 = 1, a(4) =
(5*2^3 - 1) / 3 =13, a(5) = (2^4-1)/3 = 5, a(6) = (5*2^5 - 1) / 3 =53, a(7) =
(2^6-1)/3 =21.
I would like to format this at least like
==================================================================================
Comments: Remainders for classes m of integers n (mod 2^(m+1)) which divide the
integers in 2 groups after one Collatz (3x+1)-transformation.
With one 3x+1-transformation
T(x;p) := x'= (3x+1)/2^p
all numbers of the form
x = i*2^N +a(N)
-> x' = i*6 + 1 for odd N>2,
-> x' = i*6 + 5 for even N.
Thus
x = 4*i + 3 -> x' = 6*i + 5, x = 8*i + 1 -> x' = 6*i + 1,
x =16*i +13 -> x' = 6*i + 5, x = 32*i + 5 -> x' = 6*i + 1,
x =64*i +53 -> x' = 6*i + 5, x =128*i +21 -> x' = 6*i + 1,
....
all with "i" as a free parameter >=0 covering all natural numbers
Example: a(1) = (2^0-1)/3 = 0, a(2) = (5*2^1 - 1) / 3 = 3,
a(3) = (2^2-1)/3 = 1, a(4) = (5*2^3 - 1) / 3 =13,
a(5) = (2^4-1)/3 = 5, a(6) = (5*2^5 - 1) / 3 =53,
a(7) = (2^6-1)/3 =21.
....
==================================================================================
but I am not sure I recall right how to fix linebreaks and to adjust indentation
(is linebreak ctrl-return or shift-return or... and hard spaces at the left?)
(windows OS, standard german keyboard) - I think I must have overseen something,
when I submitted this comment/example.
Just a hint?
Gottfried Helms
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