A029772 Every digit that appears in k also appears at least once in k^2.

0, 1, 5, 6, 10, 11, 25, 27, 50, 55, 60, 63, 64, 66, 74, 76, 95, 96, 99, 100, 101, 105, 110, 111, 112, 115, 116, 125, 139, 142, 199, 205, 211, 222, 225, 232, 250, 255, 261, 270, 275, 277, 278, 285, 288, 305, 323, 363, 364, 366, 371, 376, 405, 421

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Examples

			55 is in the list because 55^2 = 3025 and 5 appears in 3025.
323 is in the list because 323^2 = 104329 and 2, 3 appear in 104329.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

See A046827, where it is required that the digits of n appear in n^2 at least as often as they appear in n.

Programs

Magma

[n: n in [0..500] | Intseq(n) subset Intseq(n^2)]; // Bruno Berselli, Aug 01 2013

Mathematica

d[n_]:=IntegerDigits[n]; Select[Range[0,421],Complement[d[#],d[#^2]]=={}&] (* Jayanta Basu, Jun 02 2013 *)

Python

from itertools import count, islice
def A029772_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n:set(str(n)) <= set(str(n**2)), count(max(startvalue,0)))
A029772_list = list(islice(A029772_gen(),20)) # Chai Wah Wu, Apr 03 2023