prime sequence

Wed Feb 23 16:11:39 CET 2005

Hi!   You said, the other day:

    Are they fit to OEIS?
    If so, I will format them.

Me:  Yes, please do so!

Neil
>From seqfan-owner at ext.jussieu.fr  Thu Feb 17 04:29:36 2005
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>Subject: prime sequence
>Date: Thu, 17 Feb 2005 18:18:29 +0900
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>    Neil
>
>    These are some prime related sequences.
>    Are they fit to OEIS?
>    If so, I will format them.
>
>    %S A000001     2, 1, 2, 1, 5, 3, 8, 4, 3, 14
>    %N A000001    [Prime(n)/(Prime(n+1)-Prime(n))]
>
>    This is reciprocal number of a distance between adjacent primes
>
>    %S A000002    0, -1, 1, -1, 1, -1, -1, 2, -2,
>    %N A000002    Prime(n)-(Prime(n+1)+Prime(n-1))/2
>                        OffSet 5
>
>    I think that it represents a distance of Prime(n) and linear sequence.
>    I awoke that it is -1/2*{the difference of A001223}
>
>    %S A000003    0, 1, 2, 1, 2, 2, 4, 3, 2, 2, 1,
>    %N A000003    f(m)=(m+1)/2^r , a(n)={minimal k such that f^k 
>(Prime(n))=1}
>                        f(f(f(f(17))))=1 , so a(17)=4
>
>    %S A000004    2, 1, 3, 2, 1, 1, 3, 1, 5, 1,
>    %N A000004    2^a(n) is the largest power of two dividing (Prime(n)+1)
>
>    It appears when we use P+1 prime test.
>
>    Yasutoshi
> 
>
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><!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
><HTML><HEAD>
><META http-equiv=3DContent-Type content=3D"text/html; =
>charset=3Diso-2022-jp">
><META content=3D"MSHTML 6.00.2900.2180" name=3DGENERATOR>
><STYLE></STYLE>
></HEAD>
><BODY bgColor=3D#ffffff>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>    Neil =
></FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2></FONT> </DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>    These are =
>some prime=20
>related sequences.</FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>    Are =
>they fit to=20
>OEIS?</FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>    If so, I =
>will format=20
>them.</FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic"=20
>size=3D2>    </FONT> </DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>    %S=20
>A000001     2, 1, 2, 1, 5, 3, 8, 4, 3,=20
>14<BR>    %N A000001   =20
>[Prime(n)/(Prime(n+1)-Prime(n))]</FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic"=20
>size=3D2>          &nbs=
>p;           &nbsp=
>;  </FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>    This is =
>reciprocal=20
>number of a distance between adjacent primes</FONT></DIV>
><DIV> </DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>    =
></FONT><FONT=20
>face=3D"MS UI Gothic" size=3D2>%S A000002    0, -1, 1, =
>-1, 1, -1, -1,=20
>2, -2, <BR>    %N A000002   =20
>Prime(n)-(Prime(n+1)+Prime(n-1))/2   =20
><BR>           &nb=
>sp;           =20
>OffSet 5  </FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2></FONT> </DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>    I think =
>that it=20
>represents a distance of Prime(n) and linear sequence.</FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>    I awoke =
>that it is=20
>-1/2*{the difference of A001223}</FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>  </FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>    %S=20
>A000003    0, 1, 2, 1, 2, 2, 4, 3, 2, 2, 1, =20
><BR>    %N A000003    f(m)=3D(m+1)/2^r ,=20
>a(n)=3D{minimal k such that f^k (Prime(n))=3D1}  =20
><BR>           &nb=
>sp;           =20
>f(f(f(f(17))))=3D1 , so a(17)=3D4 </FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2></FONT> </DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>    %S=20
>A000004    2, 1, 3, 2, 1, 1, 3, 1, 5, 1, =
><BR>   =20
>%N A000004    2^a(n) is the largest power of two dividing =
>
>(Prime(n)+1)    </FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>    =
></FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>    It appears =
>when we=20
>use P+1 prime test.</FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2></FONT> </DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>    =
>Yasutoshi</FONT></DIV>
><DIV><FONT face=3D"MS UI Gothic" size=3D2>   =20
></FONT></DIV></BODY></HTML>
>
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