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A246561
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Least number k such that k concatenated with n is a cube, or 0 if no such k exists.
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1
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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
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OFFSET
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1,1
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COMMENTS
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a(n) = 0 if and only if n is in A246449.
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LINKS
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EXAMPLE
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512 is the smallest cube ending with digit 2, so a(2) = 51.
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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a(27), a(29) and a(43) corrected by Chai Wah Wu, Feb 16 2023
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STATUS
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approved
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