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

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

Author

Derek Orr, Aug 29 2014

Keywords

• nonn
• look
• base

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A000578, A246449, A245631.

Programs

PARI

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))

Python

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

Extensions

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