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A360570 Numbers m such that m concatenated with k produces a cube for some 0 <= k <= m. 1
6, 12, 21, 34, 49, 51, 58, 68, 72, 92, 100, 106, 121, 133, 138, 156, 172, 175, 195, 196, 219, 243, 262, 274, 297, 327, 337, 359, 373, 405, 409, 428, 466, 491, 506, 531, 548, 551, 583, 593, 614, 658, 681, 685, 689, 740, 753, 778, 800, 804, 830, 851, 857, 884 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers k such that A243092(k) <> A245631(k).
LINKS
EXAMPLE
64 = 4^3 is a cube and 4 <= 6, thus 6 is a term.
343 = 7^3 is a cube and 3 <= 34, thus 34 is a term.
1000 = 10^3 is a cube and 0 <= 100, thus 100 is a term.
5359375 = 175^3 is a cube and 375 <= 5359, thus 5359 is a term.
MAPLE
filter:= proc(n) local d, a, b, r, rmin, i;
for d from 1 to ilog10(n)+1 do
a:=ceil((10^d*n)^(1/3));
b:= floor((10^d*(n+1))^(1/3));
if d = 1 then rmin:= 0 else rmin:= 10^(d-1) fi;
for i from a to b do
r:= i^3 -10^d*n;
if r >= min(10^d, n+1) then break fi;
if r < rmin then next fi;
return true
od
od;
false
end proc:
select(filter, [$1..1000]); # Robert Israel, Feb 22 2023
PROG
(Python)
from itertools import count, islice
from sympy import integer_nthroot
def A360570_gen(startvalue=1): # generator of terms >= startvalue
for n in count(max(startvalue, 1)):
if integer_nthroot(m:=10*n, 3)[1]:
yield n
else:
a = 1
while (k:=(integer_nthroot(a*(m+1)-1, 3)[0]+1)**3-m*a)>=10*a:
a *= 10
if a > n:
break
else:
if k <= n:
yield n
A360570_list = list(islice(A360570_gen(), 20))
(PARI) is(n) = { for (k=0, n, if (ispower(n*10^max(1, #digits(k))+k, 3), return (1))); return (0) } \\ Rémy Sigrist, Feb 20 2023
CROSSREFS
Sequence in context: A371145 A370989 A055458 * A178733 A344033 A266085
KEYWORD
nonn,base
AUTHOR
Chai Wah Wu, Feb 20 2023
STATUS
approved

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)