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

0, 9, 99, 972, 999, 9900, 9999, 39024, 60975, 99999, 168399, 307692, 467775, 532224, 692307, 831600, 972972, 999999, 9946224, 9999999, 11678832, 12328767, 18797427, 19584972, 32618124, 42245775, 47819475, 52180524, 57754224, 67381875, 80415027, 81202572

Offset

1,2

Comments

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.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

972972 has complement 27027 (the leading 0 is ignored). 972972 * 27027 = 162162^2, so 972972 is a term of the sequence.

Mathematica

j[n_] := 9 - n; Do[If[IntegerQ[Sqrt[n*FromDigits[Map[j, IntegerDigits[n]]]]], Print[n]], {n, 1, 10^6}]
Select[Range[0, 81203000], IntegerQ[Sqrt[# FromDigits[9-IntegerDigits[ #]]]]&] (* Harvey P. Dale, Jun 26 2021 *)

Prog

(PARI) isok(n) = {d = digits(n); nd = vector(#d, k, 9-d[k]); issquare(n*fromdigits(nd)); }

Crossrefs

Cf. A061601 (9's complement).

A002283 is a subsequence.

Sequence in context: A100681 A043044 A222729 * A250603 A221579 A320075

Adjacent sequences: A068997 A068998 A068999 * A069001 A069002 A069003

Keyword

base,nonn

Author

Joseph L. Pe, Mar 20 2002

Extensions

More terms from Robert G. Wilson v, Apr 08 2002

a(1), a(21)-a(32) from Giovanni Resta, Apr 14 2017

Status

approved