A256630 Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 4 as largest digit.

142201, 1422010, 11141110, 11411110, 11412021, 14220100, 20323421, 21024111, 101203421, 110141011, 110142201, 111411100, 114111100, 114120210, 120013421, 141433102, 142201000, 203234210, 210241110, 1012034210, 1101410011, 1101410110, 1101422010, 1114111000

Offset: 1

Author

Felix Fröhlich, Apr 05 2015

Keywords

• nonn
• base

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A256631, A256633, A256634, A256708, A256709, A256889.

Subsequence of A136810.

Programs

Mathematica

fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {5, 9}] == 0, c[[4]] > 0, c[[10]] > 0]]; Select[Range@ 10000000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 12 2015 *)

PARI

is(n) = vecmin(digits(n))==0 && vecmin(digits(n^2))==0 && vecmax(digits(n))==4 && vecmax(digits(n^2))==4

Python

from itertools import product
A256630_list = []
for l in range(11):
    for a in ('1','2','3','4'):
        for b in product('01234',repeat = l):
            for c in ('0','1','2'):
                s = a+''.join(b)+c
                if '0' in s and '4' in s:
                    n = int(s)
                    s2 = set(str(n**2))
                    if {'0','4'} <= s2 <= {'0','1','2','3','4'}:
                        A256630_list.append(n)
print(A256630_list) # Chai Wah Wu, Apr 17 2015

Extensions

More terms from Alois P. Heinz, Apr 16 2015