A045620 Numbers k such that digits of k^3 include digits of k^2.

0, 1, 5, 10, 25, 50, 65, 100, 146, 250, 405, 500, 510, 521, 615, 650, 768, 945, 965, 1000, 1004, 1040, 1050, 1085, 1126, 1145, 1203, 1216, 1219, 1222, 1452, 1460, 1476, 1480, 1482, 1638, 1706, 1878, 2002, 2020, 2199, 2204, 2260, 2276, 2326, 2450, 2470, 2476

Offset: 1

Author

Erich Friedman

Keywords

• easy
• nonn
• base

Examples

			a(8) = 146 because 146^3 = 3112136 includes all digits of 146^2 = 21316.
		

Crossrefs

Cf. A029772, A046827, A046829.

Programs

Python

from itertools import count, islice
from collections import Counter
def A045620_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda k:Counter(str(m:=k**2))<=Counter(str(k*m)),count(max(startvalue,0)))
A045620_list = list(islice(A045620_gen(),20)) # Chai Wah Wu, Apr 03 2023

Extensions

Edited by N. J. A. Sloane, Nov 01 2007, at the suggestion of Alexander R. Povolotsky