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A246449 Numbers k such that no cube can end in k (in the sense of the respective decimal expansions).

%I A246449 #27 Jun 24 2025 10:45:31
%S A246449 10,14,15,18,20,22,26,30,34,35,38,40,42,45,46,50,54,55,58,60,62,65,66,
%T A246449 70,74,78,80,82,85,86,90,94,95,98,100,102,105,106,108,110,114,115,116,
%U A246449 118,120,122,124,126,130,132,134,135,138,140,142,145,146,148,150,154,155
%N A246449 Numbers k such that no cube can end in k (in the sense of the respective decimal expansions).
%C A246449 Complement of A246422.
%C A246449 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
%H A246449 Robert Israel, <a href="/A246449/b246449.txt">Table of n, a(n) for n = 1..10000</a>
%p A246449 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
%o A246449 (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
%o A246449 (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
%o A246449 (Python)
%o A246449 from sympy import nthroot_mod
%o A246449 from itertools import count, islice
%o A246449 def A246449_gen(startvalue=0): # generator of terms >= startvalue
%o A246449     return filter(lambda n: nthroot_mod(n,3,10**(len(str(n)))) is None, count(max(startvalue,0)))
%o A246449 A246449_list = list(islice(A246449_gen(),20)) # _Chai Wah Wu_, Feb 16 2023
%Y A246449 Cf. A246422.
%K A246449 nonn,base
%O A246449 1,1
%A A246449 _Derek Orr_, Aug 26 2014
%E A246449 Corrected by _Robert Israel_, Jan 26 2020
%E A246449 Name edited and incorrect PARI program deleted by _M. F. Hasler_, Jan 26 2020