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A045913 Kaprekar numbers: numbers k such that k = q + r and k^2 = q*10^m + r, for some m >= 1, q >= 0 and 0 <= r < 10^m. Here q and r must both have the same number of digits.

%I A045913 #51 Feb 16 2025 08:32:38
%S A045913 1,9,45,55,703,4950,5050,7272,7777,77778,82656,318682,329967,351352,
%T A045913 356643,390313,461539,466830,499500,500500,533170,538461,609687,
%U A045913 643357,648648,670033,681318,791505,812890,818181,851851,857143,4444444,4927941,5072059,5555556,11111112,36363636,38883889,44363341,44525548,49995000,50005000
%N A045913 Kaprekar numbers: numbers k such that k = q + r and k^2 = q*10^m + r, for some m >= 1, q >= 0 and 0 <= r < 10^m. Here q and r must both have the same number of digits.
%C A045913 A variant of Kaprekar's original definition (A006886).
%D A045913 D. R. Kaprekar, On Kaprekar numbers, J. Rec. Math., 13 (1980-1981), 81-82.
%D A045913 D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, NY, 1986, p. 151.
%H A045913 Jinyuan Wang, <a href="/A045913/b045913.txt">Table of n, a(n) for n = 1..30047</a>
%H A045913 D. E. Iannucci, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/iann2a.html">The Kaprekar numbers</a>, J. Integer Sequences, Vol. 3, 2000, #1.2.
%H A045913 Rosetta Code, <a href="http://rosettacode.org/wiki/Kaprekar_numbers">Kaprekar numbers</a>
%H A045913 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KaprekarNumber.html">Kaprekar Number</a>
%H A045913 Wikipedia, <a href="http://en.wikipedia.org/wiki/Kaprekar_number">Kaprekar number</a>
%H A045913 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%e A045913 703 is Kaprekar because 703 = 494 + 209, 703^2 = 494209.
%e A045913 11111112^2 = 123456809876544 = (1234568 + 9876544)^2. The two "halves" of the square have the same length here, although it's not m but rather m - 1.
%Y A045913 Cf. A006886, A037042, A053394, A053395, A053396, A053397, A003052, A248353.
%K A045913 nonn,base,easy
%O A045913 1,2
%A A045913 _N. J. A. Sloane_
%E A045913 More terms from _Michel ten Voorde_, Apr 13 2001
%E A045913 Definition clarified by _Reinhard Zumkeller_, Oct 05 2014
%E A045913 Definition modified and terms corrected by _Max Alekseyev_, Aug 06 2017