A246422 Numbers in which cubes may end (in base 10).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 16, 17, 19, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 36, 37, 39, 41, 43, 44, 47, 48, 49, 51, 52, 53, 56, 57, 59, 61, 63, 64, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 81, 83, 84, 87, 88, 89, 91, 92, 93, 96, 97, 99, 101, 103, 104, 107, 109, 111, 112, 113, 117

Offset: 1

Author

Derek Orr, Aug 25 2014

Keywords

• nonn
• base

Examples

			33 is a member because 77^3 = 456533 is a cube ending in 33.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..5065

Crossrefs

Cf. A238712, A246449.

Programs

Mathematica

Union@Flatten@Table[Mod[i^3, 10^n], {n, 3}, {i, 10^n}] (* Ivan Neretin, Aug 30 2015*)

PARI

v=[];for(k=1,10^3,for(m=1,3, v=concat(v,k^3%10^m)));v=vecsort(v,,8)

PARI

a=[]; for(m=1, 3, a=setunion(a, Set(vector(10^m, n, n^3)%10^m))); a

Python

from itertools import count, islice
from sympy import nthroot_mod
def A246422_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n:len(nthroot_mod(n,3,10**(len(str(n))))),count(max(startvalue,0)))
A246422_list = list(islice(A246422_gen(),20)) # Chai Wah Wu, Feb 16 2023

Extensions

Corrected by Ivan Neretin, Mar 03 2016