OFFSET
1,1
COMMENTS
No other terms below 3.16*10^20 (derived from A018884).
REFERENCES
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 109, p. 38, Ellipses, Paris 2008.
R. K. Guy, Unsolved Problems in Number Theory, F24.
LINKS
Michael Geißer, Theresa Körner, Sascha Kurz, and Anne Zahn, Squares with three digits, arXiv:2112.00444 [math.NT], 2021.
Eric Weisstein's World of Mathematics, Square Number.
FORMULA
A043537(a(n)) = 2. [Reinhard Zumkeller, Aug 05 2010]
MATHEMATICA
Select[Range[100000], Length[DeleteCases[DigitCount[#^2], 0]]==2 && !Divisible[ #, 10]&] (* Harvey P. Dale, Aug 15 2013 *)
Reap[For[n = 4, n < 10^5, n++, id = IntegerDigits[n^2]; If[FreeQ[id, {_, 0 ...}], If[Length[Union[id]] == 2, Sow[n]]]]][[2, 1]] (* Jean-François Alcover, Sep 30 2016 *)
PROG
(Python)
from gmpy2 import is_square, isqrt
from itertools import combinations, product
A016070_list = []
for g in range(2, 20):
....n = 2**g-1
....for x in combinations('0123456789', 2):
........if not x in [('0', '1'), ('0', '4'), ('0', '9')]:
............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):
........................A016070_list.append(isqrt(z))
CROSSREFS
KEYWORD
nonn,nice,base,more,hard
AUTHOR
STATUS
approved