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 A016070 Numbers n such that n^2 contains exactly 2 different digits, excluding 10^m, 2*10^m, 3*10^m. 5
 4, 5, 6, 7, 8, 9, 11, 12, 15, 21, 22, 26, 38, 88, 109, 173, 212, 235, 264, 3114, 81619 (list; graph; refs; listen; history; text; internal format)
 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 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)) A016070_list = sorted(A016070_list) # Chai Wah Wu, Nov 03 2014 CROSSREFS Cf. A016069, A018884, A018885. Sequence in context: A173888 A341051 A120181 * A299536 A321025 A047569 Adjacent sequences:  A016067 A016068 A016069 * A016071 A016072 A016073 KEYWORD nonn,nice,base,more,hard AUTHOR STATUS approved

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Last modified April 11 18:59 EDT 2021. Contains 342888 sequences. (Running on oeis4.)