The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors 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
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
Sequence in context: A162054 A289486 A245361 * A067354 A344899 A148877
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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 20 08:57 EDT 2024. Contains 372710 sequences. (Running on oeis4.)