login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A253596 Number n such that A002313(m) is the greatest prime divisor of n^2+1 and A002313(m+1) is the greatest prime divisor of (n+1)^2+1 for some m. 0
1, 7, 31, 293, 1936, 2244, 4158, 5744, 11573, 25242, 285202, 339354 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A002313 contains the primes congruent to 1 or 2 modulo 4.

The corresponding indices m in A002313 are 1, 2, 6, 13, 69, 65, 322, 199, 130, 46, 1471, 866,...

The corresponding primes A002313(m) are 2, 5, 37, 101, 809, 761, 4877, 2777, 1709, 509, 26821, 14957,...

LINKS

Table of n, a(n) for n=1..12.

EXAMPLE

31 is in the sequence because 31^2+1 = 2*13*37 and 32^2+1 = 5*5*41 with the property that 37 = A002313(6) and 41 = A002313(7).

MAPLE

with(numtheory): nn:=500000:print(1):

for n from 1 to nn do:

   p:=n^2+1:x:=factorset(p):n0:=nops(x):p1:=x[n0]:

   q:=(n+1)^2+1:y:=factorset(q):n1:=nops(y):p2:=y[n1]:ii:=0:

     for j from 2 by 2 to 1000 while(ii=0) do:

      pp:=p1+j:

      if type(pp, prime)=true and irem(pp, 4)=1

      then

      p3:=pp:ii:=1:

      else

      fi:

    od:

    if p3=p2

    then

    print(n):

     else

     fi:

    od:

MATHEMATICA

lst={}; Do[If[Mod[Prime[i], 4]==1||Mod[Prime[i], 4]==2, AppendTo[lst, Prime[i]]], {i, 1, 1000}]; Do[Do[If[FactorInteger[n^2+1][[-1]][[1]]==Part[lst, j]&&FactorInteger[(n+1)^2+1][[-1]][[1]]==Part[lst, j+1], Print[n]], {n, 1, 20000}], {j, 1, 999}]

CROSSREFS

Cf. A002313, A014442.

Sequence in context: A333735 A221875 A143564 * A298958 A153028 A276667

Adjacent sequences:  A253593 A253594 A253595 * A253597 A253598 A253599

KEYWORD

nonn,more

AUTHOR

Michel Lagneau, Jan 05 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 8 05:55 EDT 2020. Contains 333312 sequences. (Running on oeis4.)