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

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

Author

Derek Orr, Aug 26 2014

Keywords

• nonn
• base

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

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A246422.

Programs

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

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: nthroot_mod(n,3,10**(len(str(n)))) is None, count(max(startvalue,0)))
A246449_list = list(islice(A246449_gen(),20)) # Chai Wah Wu, Feb 16 2023

Extensions

Corrected by Robert Israel, Jan 26 2020

Name edited and incorrect PARI program deleted by M. F. Hasler, Jan 26 2020