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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A248527 Numbers n such that the smallest prime divisor of n^2+1 is 13. 11
34, 44, 60, 70, 86, 96, 164, 174, 190, 200, 216, 226, 294, 304, 320, 330, 346, 356, 424, 434, 450, 460, 476, 486, 554, 564, 580, 590, 606, 616, 684, 694, 710, 720, 736, 746, 814, 824, 840, 850, 866, 876, 944, 954, 970, 980, 996, 1006, 1074, 1084, 1100, 1110 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Or numbers n such that the smallest prime divisor of A002522(n) is A002313(3).

a(n) == 8 (mod 26) if n is odd and a(n) == 18 (mod 26) if n is even.

It is interesting to observe that a(n) is given by a linear formula (see the formula below).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

{a(n)} = {8+(k + m)*26} union {18+(k + m)*26} for m = 0, 5, 10,...,5p,... and k = 1, 2, 3 (values in increasing order).

EXAMPLE

34 is in the sequence because 34^2+1= 13*89.

MAPLE

* first program *

with(numtheory):p:=13:

   for n from 1 to 1000 do:

    if factorset(n^2+1)[1] = p then printf(`%d, `, n):

    else

    fi:

   od:

* second program using the formula*

for n from 0 to 100 by 5 do:

   for k from 1 to 3 do:

     x:=8+(k+n)*26:y:=18+(k+n)*26:

     printf(`%d, `, x):printf(`%d, `, y):

   od:

  od:

MATHEMATICA

lst={}; Do[If[FactorInteger[n^2+1][[1, 1]]==13, AppendTo[lst, n]], {n, 2, 2000}]; lst

p = 13; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[1200], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)

PROG

(PARI) isok(n) = factor(n^2+1)[1, 1] == 13; \\ Michel Marcus, Oct 08 2014

(MAGMA) [n: n in [2..3000] | PrimeDivisors(n^2+1)[1] eq 13]; // Bruno Berselli, Oct 08 2014

CROSSREFS

Cf. A002522, A089120, A002313.

Sequence in context: A044020 A217276 A076772 * A206262 A302457 A063470

Adjacent sequences:  A248524 A248525 A248526 * A248528 A248529 A248530

KEYWORD

nonn

AUTHOR

Michel Lagneau, Oct 08 2014

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 December 5 05:36 EST 2021. Contains 349530 sequences. (Running on oeis4.)