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 A029783 Exclusionary squares: numbers n such that no digit of n is present in n^2. 17

%I

%S 2,3,4,7,8,9,17,18,22,24,29,33,34,38,39,44,47,53,54,57,58,59,62,67,72,

%T 77,79,84,88,92,94,144,157,158,173,187,188,192,194,209,212,224,237,

%U 238,244,247,253,257,259,307,313,314,333,334,338,349,353,359

%N Exclusionary squares: numbers n such that no digit of n is present in n^2.

%C Complement of A189056; A076493(a(n)) = 0. - _Reinhard Zumkeller_, Apr 16 2011

%C A258682(a(n)) = a(n)^2. - _Reinhard Zumkeller_, Jun 07 2015

%D Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 60.

%H Giovanni Resta, <a href="/A029783/b029783.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Reinhard Zumkeller)

%H Cliff Pickover et al, <a href="https://groups.google.com/forum/#!topic/rec.puzzles/ubSItPD_DGY">Exclusionary Squares and Cubes</a>, rec.puzzles topic on google groups, January 2002

%e From _M. F. Hasler_, Oct 16 2018: (Start)

%e It is easy to construct infinite subsequences of the form S(a,b)(n) = a*R(n) + b, where R(n) = (10^n-1)/9 is the repunit of length n. These are:

%e S(3,0) = (3, 33, 333, ...), S(3,1) = (4, 34, 334, 3334, ...), S(3,5) = (8, 38, 338, ...), S(6,0) = (6, 66, 666, ...), S(6,1) = (7, 67, 667, ...), S(6,6) = (72, 672, 6672, ...) (excluding n=1), S(6,7) = (673, 6673, ...) (excluding also n=2 here) and S(6,-7) = (59, 659, 6659, ...). (End)

%t Select[Range[1000], Intersection[IntegerDigits[ # ], IntegerDigits[ #^2]] == {} &] (* _Tanya Khovanova_, Dec 25 2006 *)

%o a029783 n = a029783_list !! (n-1)

%o a029783_list = filter (\x -> a258682 x == x ^ 2) [1..]

%o -- _Reinhard Zumkeller_, Jun 07 2015, Apr 16 2011

%o (PARI) is_A029783(n)=!#setintersect(Set(digits(n)),Set(digits(n^2))) \\ _M. F. Hasler_, Oct 16 2018

%Y Cf. A059930 = numbers n such that n and n^2 combined use different digits, A112736 = numbers whose squares are exclusionary.

%Y Cf. A029784, A029785, A029786, A111116, A113316, A189056, A076493, A258682.

%K nonn,base

%O 1,1

%A _Patrick De Geest_

%E Definition slightly reworded on suggestion of _Franklin T. Adams-Watters_ by _M. F. Hasler_, Oct 16 2018

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Last modified May 26 22:58 EDT 2020. Contains 334634 sequences. (Running on oeis4.)