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Gaps in {sigma(n)}...
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Collins
P versus NP
P versus NP

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Gabon
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#1
Gaps in {sigma(n)}...
Let S=\{\sigma(n),n\in\mathbb{N}^*\}.
For all L\in\mathbb{N}, can we find a\in\mathbb{N} such that [a,a+L] \cap S=\emptyset?

Related question (solved by Myth): here

PostPosted: Wed Feb 16, 2005 10:37 am
Bojan Basic
Poincare Conjecture
Poincare Conjecture

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#2
Here is my advance, not much but is better than nothing:

Let L be a number such that \{a,a+1,...,a+L-1\}\cap S=\emptyset for some a. Then we know the following:

L=1\Rightarrow a_{min}=2
L\in\{2,3\}\Rightarrow a_{min}=9
L\in\{4,5\}\Rightarrow a_{min}=49
L\in\{6,7,8,9\}\Rightarrow a_{min}=423
L\in\{10,11\}\Rightarrow a_{min}=1333
L\geq 12\Rightarrow a_{min}>1333

Does somebody want to continue? Smile

PostPosted: Thu Mar 17, 2005 10:51 pm
Bojan Basic
Poincare Conjecture
Poincare Conjecture

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#3
I have just found an interesting reference related to this problem. Check http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A109322
_________________
- Why do mathematicians get Christmas and Halloween mixed up?
- Because Dec. 25 = Oct. 31.

PostPosted: Tue Sep 13, 2005 1:15 pm
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