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A246449
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Numbers n such that no cube can end in n (in the sense of the respective decimal expansions).
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5
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10, 14, 15, 18, 20, 22, 26, 30, 34, 35, 38, 40, 42, 45, 46, 50, 54, 55, 58, 60, 62, 65, 66, 70, 74, 78, 80, 82, 85, 86, 90, 94, 95, 98, 100, 102, 105, 106, 108, 110, 114, 115, 116, 118, 120, 122, 124, 126, 130, 132, 134, 135, 138, 140, 142, 145, 146, 148, 150, 154, 155
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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The terms with n digits are the complement in [10^(n-1) .. 10^n-1] of the set of residues of k^3 mod 10^n for 10^((n-1)/3) < k < 10^n. - M. F. Hasler, Jan 26 2020
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LINKS
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MAPLE
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seq(op(sort(convert({$10^(d-1)..10^d-1} minus map(t -> t^3 mod 10^d, {$0..10^d-1}), list))), d=1..3); # Robert Israel, Jan 26 2020
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PROG
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(PARI) v=vector(1000); for(k=1, 10^4, my(q=k^3, w=digits(q)); for(j=0, 2, v[1+fromdigits(w[#w-j..#w])]++)); for(k=1, 160, if(v[k]==0, print1(k-1, ", "))) \\ Hugo Pfoertner, Jan 26 2020
(PARI) A246449_row(n)=setminus([10^(n-1)..10^n-1], Set([k^3|k<-[sqrtnint(10^(n-1), 3)+1..10^n-1]]%10^n)) \\ Yields the n-digit terms. - M. F. Hasler, Jan 26 2020
(Python)
from sympy import nthroot_mod
from itertools import count, islice
def A246449_gen(startvalue=0): # generator of terms >= startvalue
return filter(lambda n:not len(nthroot_mod(n, 3, 10**(len(str(n))))), count(max(startvalue, 0)))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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Name edited and incorrect PARI program deleted by M. F. Hasler, Jan 26 2020
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STATUS
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approved
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