# A107751

Peter Pein petsie at dordos.net
Sat Oct 13 03:45:08 CEST 2007

```Hi Artur,

A107751[nmax_] :=
Length /@ Split[(Total[1 - IntegerDigits[#1, 2]] &) /@ Range[0, nmax]]

A107751[200]

Out[2]=
{1,1,1,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,
2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,
2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,
2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1}

is simple &   fast.

Enjoy,
Peter

Artur schrieb:
> I would like to ask is somebody which understand A107751 and is able
> write Mathematica procedure. I was obtained that same sequence in
> completely another problem and connection is very unexpected  I want
> check that these two are that same. My procedure is on number of factors
> of  polynomials (x^n+x+1) :
> Table[Length[FactorList[x^n + x + 1]] - 1, {n, 0, 200}]
> {1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1,
> 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1,
> 2, 1,
> 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1,
> 1, 2,
> 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2,
> 1, 1,
> 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1,
> 2, 1,
> 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1,
> 1, 2,
> 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2,
> 1, 1,
> 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2}
>
> I will be greatfull for procedure or explanation that these two
> different matters are that same
>
> Best wishes
> Artur
>
>

Hello SeqFans,

I just submitted a sequence that looks cute.

1,3,6,9,12,16,21,
%N A000001 a(n) is the maximum number of points on a n by n square grid such that no 4 points form a rectangle having sides parallel to the sides of the grid.
%C A000001 a(7) is presented as a puzzle in Mathematical Gems III by Ross Honsberger on page 4.

I did the calculations manually - can someone check them and continue the sequence?

Tanya

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Need personalized email and website? Look no further. It's easy

Bob, Jonathan:

%S A115057 2,5,11,17,25,30,45,67,74,82,95,111,141,177,193,208,211,223,257,277,288,
%T A115057 353,431,453,481,509,528,540,563,619,672,700,725,745,804,857,905,1003,
%U A115057 1077,1127,1199,1268,1281,1321,1354,1379,1423,1517,1607,1660,1714,1748
%N A115057 The number of (2n+1)-almost primes less than or equal to (n-th n-almost prime) * ((n\
+1)-th (n+1)-almostprime).

But it is rather artificial, don't you agree?

It seems to contribute to the dilution of the OEIS by large
numbers of ugly sequences, always contributed by the same few people.

It would be easy to send in millions of similar sequences.

The criterion should be, not "Is this sequence in the OEIS?",
but rather "Is this sequence interesting?"

Please exercise some restraint (and good judgement)!

Neil

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