A272234
Least positive integer c such that (n, c-n, c) is an abc-hit.
Original entry on oeis.org
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
Offset: 1
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.
Cf.
A272236 (corresponding values of b).
Cf.
A130512 (radicals of abc-hits).
-
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
A272239
Least positive integer b such that b > n and (n, b, n+b) is an abc-hit.
Original entry on oeis.org
8, 243, 125, 121, 27, 214369, 243, 1323, 2048, 2187, 2176, 5021863, 243, 658489, 85169, 6859, 5103, 148046875, 6125, 19663, 327680, 23882747, 2025, 1830101, 704, 3536379, 512, 50625, 19683, 75926359382369, 19652, 49, 2000000, 793071875, 4096, 313046839, 32768
Offset: 1
a(8) = 1323 because rad(8*1323*1331) = 2*21*11 = 462 < 1331, hence (8, 1323, 1331) is an abc-hit and (8, b, b+3) isn't an abc-hit for every b where 8 < b < 1323.
Cf.
A272240 (corresponding values of c).
Cf.
A272236 (analog of this sequence without assumption that n - the smallest element of the triple).
Cf.
A130512 (radicals of abc-hits).
-
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 2*a+1 do
if igcd(a,c)=1 then rc:=rad(c):
if ra*rc
-
rad(x, y, z) = my(f=factor(x*y*z)[, 1]~); prod(i=1, #f, f[i])
is_abc_hit(x, y, z) = gcd(x, y)==1 && gcd(x, z)==1 && gcd(y, z)==1 && rad(x, y, z) < z
a(n) = my(b=n+1); while(!is_abc_hit(n, b, n+b), b++); b \\ Felix Fröhlich, May 08 2016
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