A246449 -id:A246449 - cp's OEIS frontend

A077743 Smallest cube ending in n, or 0 if no such cube exists.

1, 512, 343, 64, 125, 216, 27, 8, 729, 0, 357911, 512, 4913, 0, 0, 216, 389017, 0, 59319, 0, 68921, 0, 103823, 13824, 125, 0, 27, 1728, 729, 0, 1331, 5832, 456533, 0, 0, 97336, 35937, 0, 493039, 0, 531441, 0, 343, 2744, 0, 0, 250047, 10648, 117649, 0, 132651

Offset: 1

Amarnath Murthy, Nov 20 2002

			a(1) = 4913 = 17^3, a(10) = 0.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000578, A077744, A246449.

f:= proc(n) local m,r,x;
  m:= 10^(ilog10(n)+1);
  r:= [msolve(x^3=n,m)];
  if r = [] then 0 else min(map(t -> rhs(op(t)),r))^3 fi
end proc:
map(f, [$1..100]); # Robert Israel, Mar 05 2023

a(m*10^(3k+1)) = a(m*10^(3k+2)) = 0.

More terms from Sascha Kurz, Jan 07 2003

A077744 Smallest number whose cube ends in n, or 0 if no such number exists. a(n) = A077743(n)^(1/3).

Original entry on oeis.org

1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 71, 8, 17, 0, 0, 6, 73, 0, 39, 0, 41, 0, 47, 24, 5, 0, 3, 12, 9, 0, 11, 18, 77, 0, 0, 46, 33, 0, 79, 0, 81, 0, 7, 14, 0, 0, 63, 22, 49, 0, 51, 28, 37, 0, 0, 36, 93, 0, 19, 0, 21, 0, 67, 4, 0, 0, 23, 32, 89, 0, 91, 38, 97, 0, 15, 26, 53, 0, 59, 0, 61, 0, 27, 44, 0

Offset: 1

Amarnath Murthy, Nov 20 2002

			a(13) = 17, a(10) = 0.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000578, A077743, A246449.

f:= proc(n) local m,r,x;
  m:= 10^(ilog10(n)+1);
  r:= [msolve(x^3=n,m)];
  if r = [] then 0 else min(map(t -> rhs(op(t)),r)) fi
end proc:
map(f, [$1..100]); # Robert Israel, Mar 05 2023

a(m*10^(3*k+1)) = a(m*10^(3*k+2)) = 0.

More terms from Sascha Kurz, Jan 07 2003

A246422 Numbers in which cubes may end (in base 10).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 16, 17, 19, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 36, 37, 39, 41, 43, 44, 47, 48, 49, 51, 52, 53, 56, 57, 59, 61, 63, 64, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 81, 83, 84, 87, 88, 89, 91, 92, 93, 96, 97, 99, 101, 103, 104, 107, 109, 111, 112, 113, 117

Offset: 1

Derek Orr, Aug 25 2014

			33 is a member because 77^3 = 456533 is a cube ending in 33.

Ivan Neretin, Table of n, a(n) for n = 1..5065

Cf. A238712, A246449.

Union@Flatten@Table[Mod[i^3, 10^n], {n, 3}, {i, 10^n}] (* Ivan Neretin, Aug 30 2015*)

v=[];for(k=1,10^3,for(m=1,3, v=concat(v,k^3%10^m)));v=vecsort(v,,8)

a=[]; for(m=1, 3, a=setunion(a, Set(vector(10^m, n, n^3)%10^m))); a

from itertools import count, islice
from sympy import nthroot_mod
def A246422_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n:len(nthroot_mod(n,3,10**(len(str(n))))),count(max(startvalue,0)))
A246422_list = list(islice(A246422_gen(),20)) # Chai Wah Wu, Feb 16 2023

Corrected by Ivan Neretin, Mar 03 2016

A246561 Least number k such that k concatenated with n is a cube, or 0 if no such k exists.

Original entry on oeis.org

133, 51, 34, 6, 12, 21, 2, 172, 72, 0, 3579, 5, 49, 0, 0, 2, 3890, 0, 593, 0, 689, 0, 1038, 138, 1, 0, 10927, 17, 7, 0, 13, 58, 4565, 0, 0, 973, 359, 0, 4930, 0, 5314, 0, 3, 27, 0, 0, 2500, 106, 1176, 0, 1326, 219, 506, 0, 0, 466, 8043, 0, 68, 0, 92, 0, 3007, 1574, 0, 0, 121, 327, 7049, 0, 7535, 548, 9126, 0, 33

Offset: 1

Derek Orr, Aug 29 2014

a(n) = 0 if and only if n is in A246449.

			512 is the smallest cube ending with digit 2, so a(2) = 51.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A000578, A246449, A245631.

b(n)=v=[];for(k=10^(n-1),10^n,v=concat(v,k^3%10^n));v=vecsort(v,,8);v
w=[];for(k=1,250,d=digits(k);if(vecsearch(b(#d),k),w=concat(w,k)));w=vecsort(w,,8);w;
a(n)=if(!vecsearch(w,n),return(0));if(vecsearch(w,n),j=1;s=Str(n);while(!ispower(eval(concat(Str(j),s)),3),j++);return(j))
vector(200,n,a(n))

from sympy import nthroot_mod
def A246561(n): return 0 if len(l:=nthroot_mod(n,3,(m:=10**(len(str(n)))))) == 0 else int((min(x for x in l+[d+m for d in l] if x**3>=m)**3-n)//m) # Chai Wah Wu, Feb 16 2023

a(27), a(29) and a(43) corrected by Chai Wah Wu, Feb 16 2023

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A077743 Smallest cube ending in n, or 0 if no such cube exists.

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A077744 Smallest number whose cube ends in n, or 0 if no such number exists. a(n) = A077743(n)^(1/3).

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A246422 Numbers in which cubes may end (in base 10).

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A246561 Least number k such that k concatenated with n is a cube, or 0 if no such k exists.

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