

A029783


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


17



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, 77, 79, 84, 88, 92, 94, 144, 157, 158, 173, 187, 188, 192, 194, 209, 212, 224, 237, 238, 244, 247, 253, 257, 259, 307, 313, 314, 333, 334, 338, 349, 353, 359
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OFFSET

1,1


COMMENTS

Complement of A189056; A076493(a(n)) = 0.  Reinhard Zumkeller, Apr 16 2011
A258682(a(n)) = a(n)^2.  Reinhard Zumkeller, Jun 07 2015


REFERENCES

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


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)
Cliff Pickover et al, Exclusionary Squares and Cubes, rec.puzzles topic on google groups, January 2002


EXAMPLE

From M. F. Hasler, Oct 16 2018: (Start)
It is easy to construct infinite subsequences of the form S(a,b)(n) = a*R(n) + b, where R(n) = (10^n1)/9 is the repunit of length n. These are:
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)


MATHEMATICA

Select[Range[1000], Intersection[IntegerDigits[ # ], IntegerDigits[ #^2]] == {} &] (* Tanya Khovanova, Dec 25 2006 *)


PROG

(Haskell)
a029783 n = a029783_list !! (n1)
a029783_list = filter (\x > a258682 x == x ^ 2) [1..]
 Reinhard Zumkeller, Jun 07 2015, Apr 16 2011
(PARI) is_A029783(n)=!#setintersect(Set(digits(n)), Set(digits(n^2))) \\ M. F. Hasler, Oct 16 2018


CROSSREFS

Cf. A059930 = numbers n such that n and n^2 combined use different digits, A112736 = numbers whose squares are exclusionary.
Cf. A029784, A029785, A029786, A111116, A113316, A189056, A076493, A258682.
Sequence in context: A152037 A058075 A243495 * A112736 A059930 A125965
Adjacent sequences: A029780 A029781 A029782 * A029784 A029785 A029786


KEYWORD

nonn,base


AUTHOR

Patrick De Geest


EXTENSIONS

Defnition slightly reworded on suggestion of Franklin T. AdamsWatters by M. F. Hasler, Oct 16 2018


STATUS

approved



