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A246449
Numbers n such that no cube can end in n (in the sense of the respective decimal expansions).
5
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
OFFSET
1,1
COMMENTS
Complement of A246422.
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
LINKS
MAPLE
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
PROG
(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)))
A246449_list = list(islice(A246449_gen(), 20)) # Chai Wah Wu, Feb 16 2023
CROSSREFS
Cf. A246422.
Sequence in context: A102361 A280032 A227010 * A121836 A317590 A081062
KEYWORD
nonn,base
AUTHOR
Derek Orr, Aug 26 2014
EXTENSIONS
Corrected by Robert Israel, Jan 26 2020
Name edited and incorrect PARI program deleted by M. F. Hasler, Jan 26 2020
STATUS
approved