A064827 Numbers k such that each digit of k occurs among the digits of k^2.

1, 5, 6, 10, 11, 25, 27, 50, 60, 63, 64, 74, 76, 95, 96, 100, 101, 105, 110, 125, 139, 142, 205, 250, 255, 261, 270, 275, 277, 278, 285, 305, 364, 371, 376, 405, 421, 441, 463, 472, 493, 497, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 523, 524, 525, 593, 600, 601, 602

Offset: 1

Author

Joseph L. Pe, Feb 14 2002

Keywords

• nonn
• base

Comments

That is, if n is d digits long, then each one of those d digits occurs in the digits of n^2.

Examples

			125^2 = 15625, which contains all digits of 125, so 125 is a term of the sequence.
55 is not here because 55^2 = 3025, which has only one 5.
		

Crossrefs

Cf. A046827 (essentially the same).

Programs

Mathematica

Reap[Do[a = DigitCount[n^2]; b = DigitCount[n]; If[Min[a-b] >= 0, Sow[n]], {n, 1, 10^3}]][[2,1]]

Python

from itertools import count, islice
from collections import Counter
def A064827_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda k:Counter(str(k))<=Counter(str(k**2)),count(max(startvalue,1)))
A064827_list = list(islice(A064827_gen(),20)) # Chai Wah Wu, Apr 03 2023