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!)
A272234 Least positive integer c such that (n, c-n, c) is an abc-hit. 2
9, 245, 128, 125, 32, 214375, 250, 9, 2057, 2197, 2187, 5021875, 256, 658503, 85184, 6875, 5120, 148046893, 6144, 19683, 327701, 23882769, 2048, 1830125, 729, 3536405, 32, 50653, 19712, 75926359382399, 19683, 81, 2000033, 793071909, 4131, 313046875, 32805, 2366250327 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
An abc-hit is a triple of coprime positive integers a, b, c such that a + b = c and rad(abc) < c, where rad(n) is the largest squarefree number dividing n.
LINKS
Wikipedia, abc conjecture
EXAMPLE
a(2) = 245 because rad(2*243*245) = 2*3*35 = 210 < 245, hence (2, 243, 245) is an abc-hit and (2, c-2, c) isn't an abc-triple for every c < 245.
MAPLE
rad:=n -> mul(i, i in factorset(n)):
min_c_for_a:=proc(n) local a, b, c, ra, rc;
for a to n do
ra:=rad(a):
for c from a+1 do
if igcd(a, c)=1 then rc:=rad(c):
if ra*rc<c then b:=c-a:
if ra*rc*rad(b)<c then break fi fi fi od:
print([a, b, c]) od end;
CROSSREFS
Cf. A272236 (corresponding values of b).
Cf. A120498, A130510 (possible values of c in abc-hits).
Cf. A225426 (triples of abc-hits).
Cf. A130512 (radicals of abc-hits).
Cf. A007947 (radicals).
Sequence in context: A183235 A359732 A259673 * A272240 A161159 A367541
KEYWORD
nonn
AUTHOR
Vladimir Letsko, Apr 23 2016
EXTENSIONS
More terms from Jinyuan Wang, Jun 08 2022
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 March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)