login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A247340 Numbers n such that each prime divisor of the semiprime n^2+1 is also a divisor of a^2+1 and b^2+1 respectively for some a, b < n. 2
3, 8, 30, 46, 50, 76, 100, 144, 254, 266, 274, 286, 334, 380, 456, 494, 504, 516, 520, 526, 566, 664, 670, 726, 756, 810, 836, 844, 874, 1040, 1064, 1086, 1130, 1164, 1216, 1250, 1300, 1476, 1714, 1740, 1800, 1826, 1834, 1946, 1950, 2014, 2194, 2200, 2220, 2324 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Or numbers n such that n^2+1 = p*q, p and q primes => p | a^2+1 and q | b^2+1 for some a,b < n.

Subsequence of A085722 and except the first term, a(n) is even.

The squares of the sequence are 100, 144, 3364, 6084, 7396, 10404, 24964, 45796, 47524, 68644, 71824, 93636,...

Observation : a(n) = p*q => there exists a and b such that a^2+1 = m*p and b^2+1 = m*q. (see the examples).

LINKS

Michel Lagneau, Table of n, a(n) for n = 1..1000

EXAMPLE

3^2+1 = 2*5 => 1^1+1 = 2 and 2^2+1 = 5 ;

8^2+1 = 5*13 => 3^2+1 = 2*5 and 5^2+1 = 2*13 ;

30^2+1 = 17*53 => 13^2+1=2*5*17 and 23^2+1 = 2*5*53 ;

46^2+1 = 29*73 => 17^2+1 = 2*5*29 and 27^2+1=2*5*73 ;

50^2+1 = 41*61 => 9^2+1 = 2*41 and 11^2+1 = 2*61 ;

76^2+1 = 53*109 => 23^2+1 = 2*5*53 and 33^2+1 = 2*5*109 ;

100^2+1 = 73*137 => 27^2+1=2*5*73 and 37^2+1 = 2*5*137 ;

144^2+1 = 89*233 => 55^2+1 = 2*17*89 and 89^2+1 = 2*17*233 ;

254^2+1 = 149*433 => 105^2+1 = 2*37*149 and 179^2+1 = 2*37*433 ;

266^2+1 = 173*409 => 93^2+1 = 2*5^2*173 and 143^2+1 = 2*5^2*409.

MAPLE

with(numtheory):lst:={}:

for n from 1 to 3000 do:

   x:=factorset(n^2+1):n0:=nops(x):

     for i from 1 to n0 do:

      lst:=lst union {x[i]}:

     od:

      lst1:={}:nn:=n+1:xx:=factorset(nn^2+1):nn0:=nops(xx):

        for j from 1 to nn0 do:

         lst1:=lst1 union {xx[j]}:

        od:

        if

         nn0=2

         and bigomega(nn^2+1)=2

         and {xx[1], xx[2]} intersect lst = {xx[1], xx[2]}

         then

         printf(`%d, `, n+1):

         else

        fi:

        lst:=lst union lst1:

  od:

CROSSREFS

Cf. A085722, A144255.

Sequence in context: A162054 A289486 A245361 * A067354 A148877 A148878

Adjacent sequences:  A247337 A247338 A247339 * A247341 A247342 A247343

KEYWORD

nonn

AUTHOR

Michel Lagneau, Sep 14 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 July 15 20:23 EDT 2019. Contains 325056 sequences. (Running on oeis4.)