|
|
A016069
|
|
Numbers k such that k^2 contains exactly 2 distinct digits.
|
|
18
|
|
|
4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 20, 21, 22, 26, 30, 38, 88, 100, 109, 173, 200, 212, 235, 264, 300, 1000, 2000, 3000, 3114, 10000, 20000, 30000, 81619, 100000, 200000, 300000, 1000000, 2000000, 3000000, 10000000, 20000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
10^k, 2*10^k, 3*10^k for k > 0 are terms. - Chai Wah Wu, Dec 17 2021
|
|
REFERENCES
|
R. K. Guy, Unsolved Problems in Number Theory, F24.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = ((n-1) mod 3 + 1)*10^(ceiling(n/3)-7) for n >= 34 (conjectured). - Chai Wah Wu, Dec 17 2021
|
|
EXAMPLE
|
26 is in the sequence because 26^2 = 676 contains exactly 2 distinct digits.
|
|
MATHEMATICA
|
Join[Select[Range[90000], Count[DigitCount[#^2], _?(#!=0&)]==2&], Flatten[ NestList[ 10#&, {100000, 200000, 300000}, 5]]] (* Harvey P. Dale, Mar 09 2013 *)
Select[Range[20000000], Length[Union[IntegerDigits[#^2]]]==2&] (* Vincenzo Librandi, Nov 04 2014 *)
|
|
PROG
|
(Haskell)
import Data.List (nub)
a016069 n = a016069_list !! (n-1)
a016069_list = filter ((== 2) . length . nub . show . (^ 2)) [0..]
(PARI) /* needs version >= 2.6 */
for (n=1, 10^9, if ( #Set(digits(n^2))==2, print1(n, ", ") ) );
(Python)
from gmpy2 import is_square, isqrt
from itertools import combinations, product
for g in range(2, 10):
n = 2**g-1
for x in combinations('0123456789', 2):
for i, y in enumerate(product(x, repeat=g)):
if i > 0 and i < n and y[0] != '0':
z = int(''.join(y))
if is_square(z):
(Magma) [n: n in [0..20000000] | #Set(Intseq(n^2)) eq 2]; // Vincenzo Librandi, Nov 04 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,nice
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|