cp's OEIS Frontend

A069000 Numbers k such that k * (digit complement of k) is a square.

%I A069000 #23 Jun 26 2021 17:35:35
%S A069000 0,9,99,972,999,9900,9999,39024,60975,99999,168399,307692,467775,
%T A069000 532224,692307,831600,972972,999999,9946224,9999999,11678832,12328767,
%U A069000 18797427,19584972,32618124,42245775,47819475,52180524,57754224,67381875,80415027,81202572
%N A069000 Numbers k such that k * (digit complement of k) is a square.
%C A069000 The digit complement of a digit d is 9 - d; e.g., 8 and 3 have complements 1, 6, respectively. The digit complement of a number k is the number formed by replacing each digit of k by its complement; e.g., 83 has complement 16.
%H A069000 Giovanni Resta, <a href="/A069000/b069000.txt">Table of n, a(n) for n = 1..10000</a>
%e A069000 972972 has complement 27027 (the leading 0 is ignored). 972972 * 27027 = 162162^2, so 972972 is a term of the sequence.
%t A069000 j[n_] := 9 - n; Do[If[IntegerQ[Sqrt[n*FromDigits[Map[j, IntegerDigits[n]]]]], Print[n]], {n, 1, 10^6}]
%t A069000 Select[Range[0,81203000],IntegerQ[Sqrt[# FromDigits[9-IntegerDigits[ #]]]]&] (* _Harvey P. Dale_, Jun 26 2021 *)
%o A069000 (PARI) isok(n) = {d = digits(n); nd = vector(#d, k, 9-d[k]); issquare(n*fromdigits(nd));}
%Y A069000 Cf. A061601 (9's complement).
%Y A069000 A002283 is a subsequence.
%K A069000 base,nonn
%O A069000 1,2
%A A069000 _Joseph L. Pe_, Mar 20 2002
%E A069000 More terms from _Robert G. Wilson v_, Apr 08 2002
%E A069000 a(1), a(21)-a(32) from _Giovanni Resta_, Apr 14 2017