%S A116151 1,5,23,173,2273,2273,197468,1728998,1728998

[Maximilian Hasler]

well spoken.
and it should be clear that the definition should be corrected on
http://www.research.att.com/~njas/sequences/A116151
in order to include x=2 mod 3.
(maybe simplified to "smallest positive integer such that a(n) =
p[k-1] (mod p[k]) for k=1..n, where p[k] is the k-th prime number and
p[0] = 1.")

Since I'm a bit new to this mailing list, I don't know if maxal's
e-mail is "equivalent" to filling in the form for adding the terms and
PARI code (it would be a pity not to do it), especially for this
"perfect stub" (title longer than the rest)....

Maximilian

On 4/16/07, Max Alekseyev <maxale at gmail.com> wrote:
> PARI/GP code for first 30 terms:
>
> { a(n) = lift(chinese(vector(n,i,Mod(if(i==1,1,prime(i-1)),prime(i))))) }
>
> ? vector(30,n,a(n))
> %1 = [ 1, 5, 23, 173, 2273, 2273, 452723, 6578843, 113275433,
> 3682761353, 10152454583, 5024164707833, 249908523156563,
> 5726413266646343, 345878207890067123, 15103232990013860963,
> 1905274424667036455303, 111502614383457156882293,
> 932521283899305953765183, 8790842834979573009644273,
> 10051725785115560870423121293, 498807892976103850677879002933,
> 55198768937767543284962316423143, 5396489082723284570397442676278943,
> 1051221132521927518479021097136044583,
> 224691313635237214719529929388316383373,
> 5580525693880676515420986217639985733983,
> 1180836878611216856978040546513560647148273,
> 219322806874186167087743854850419650760678223,
> 11408722679588383614218790329733132037760567423 ]
>
> Max
>
> On 4/16/07, zak seidov <zakseidov at yahoo.com> wrote:
> > More terms:
> >
> > %S A116151
> > 1,5,23,173,2273,2273,197468,1728998,1728998,447914738,10152454583,1313795640428,97783391392958,
> > 5726413266646343,38433316595821418
> >
> >
> > --- zak seidov <zakseidov at yahoo.com> wrote:
> >
> > > Dear Christian, Seqfans,
> > >
> > > My version is:
> > >
> > > %S A116151
> > > 1,5,23,173,2273,2273,197468,1728998,1728998
> > >
> > > ?,
> > > Zak
> > >
> > > %%%%%%%%%%%%%%
> > > %I A116151
> > > %S A116151 1,5,23,173,2273,2273,452723,6578843
> > > %N A116151 a(n) = smallest positive integer x
> > > satisfying the system of congruences x = 1 (mod 2),
> > > x
> > > = 3 (mod 5), x = 5 (mod 7), ..., x = p[n-1] (mod
> > > p[n]), where p[n] is the nth prime number and p[0]
> > > taken to be 1.
> > > %K A116151 nonn,new
> > > %O A116151 1,2
> > > %A A116151 Christian Bjartli
> > > (cbjartli(AT)gmail.com),
> > > Apr 14 2007
> > >
> > >
> > > __________________________________________________
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>



Straightforward duplicates:

A023727 and A043354
A087921 and A087922
A101294 and A101935
A056209 and A056157 and (maybe?) A098671
A056266 and A101019
A056252 and A101829
A057130 and A121404
A090484 and A090489
A086749 and A086750
A076671 and A076718
A077491 and A088401

Possibly the same sequence:

A123481 and A076715 (can this really just be coincidence?)
A107317 and A112667