A272236
Least positive integer b such that (n, b, n+b) is an abc-hit.
Original entry on oeis.org
8, 243, 125, 121, 27, 214369, 243, 1, 2048, 2187, 2176, 5021863, 243, 658489, 85169, 6859, 5103, 148046875, 6125, 19663, 327680, 23882747, 2025, 1830101, 704, 3536379, 5, 50625, 19683, 75926359382369, 19652, 49, 2000000, 793071875, 4096, 313046839, 32768, 2366250289
Offset: 1
a(3) = 125 because rad(3*125*128) = 3*5*2 = 31 < 128, hence (3, 125, 128) is an abc-hit and (3, b, b+3) isn't an abc-hit for every b < 125.
Cf.
A272239 (analog of this sequence taking into account that n - the smallest element of the triple).
Cf.
A272234 (corresponding values of c).
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
A272240
Least positive integer c such that (n, c-n, c) is an abc-hit and n is the least number in the triple.
Original entry on oeis.org
9, 245, 128, 125, 32, 214375, 250, 1331, 2057, 2197, 2187, 5021875, 256, 658503, 85184, 6875, 5120, 148046893, 6144, 19683, 327701, 23882769, 2048, 1830125, 729, 3536405, 539, 50653, 19712, 75926359382399, 19683, 81, 2000033, 793071909, 4131, 313046875, 32805
Offset: 1
a(8) = 1331 because rad(8*1323*1331) = 2*21*11 = 462 < 1331, hence (8, 1323, 1331) is an abc-hit and (8, c-8, c) isn't an abc-hit for every c satisfying unequalities c < 1331 and 8 < c-8.
Cf.
A272239 (corresponding values of b).
Cf.
A272234 (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
Showing 1-2 of 2 results.
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