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 A016069 Numbers k such that k^2 contains exactly 2 distinct digits. 17
 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 Robert G. Wilson v, Table of n, a(n) for n = 1..81 Eric Weisstein's World of Mathematics, Square Number 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..] -- Reinhard Zumkeller, Apr 14 2011 (PARI) /* needs version >= 2.6 */ for (n=1, 10^9, if ( #Set(digits(n^2))==2, print1(n, ", ") ) ); /* Joerg Arndt, Mar 09 2013 */ (Python) from gmpy2 import is_square, isqrt from itertools import combinations, product A016069_list = [] 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):                     A016069_list.append(int(isqrt(z))) A016069_list = sorted(A016069_list) # Chai Wah Wu, Nov 03 2014 (MAGMA) [n: n in [0..20000000] | #Set(Intseq(n^2)) eq 2]; // Vincenzo Librandi, Nov 04 2014 CROSSREFS Cf. A016070, A018884, A018885. Sequence in context: A191842 A299544 A039174 * A194283 A299546 A039128 Adjacent sequences:  A016066 A016067 A016068 * A016070 A016071 A016072 KEYWORD nonn,base,nice AUTHOR STATUS approved

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Last modified January 20 13:25 EST 2022. Contains 350472 sequences. (Running on oeis4.)