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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. 8
 1, 9, 45, 55, 703, 4950, 5050, 7272, 7777, 77778, 82656, 318682, 329967, 351352, 356643, 390313, 461539, 466830, 499500, 500500, 533170, 538461, 609687, 643357, 648648, 670033, 681318, 791505, 812890, 818181, 851851, 857143, 4444444, 4927941, 5072059, 5555556, 11111112, 36363636, 38883889, 44363341, 44525548, 49995000, 50005000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A variant of Kaprekar's original definition (A006886). REFERENCES D. R. Kaprekar, On Kaprekar numbers, J. Rec. Math., 13 (1980-1981), 81-82. D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, NY, 1986, p. 151. LINKS Jinyuan Wang, Table of n, a(n) for n = 1..30047 D. E. Iannucci, The Kaprekar numbers, J. Integer Sequences, Vol. 3, 2000, #1.2. Rosetta Code, Kaprekar numbers Eric Weisstein's World of Mathematics, Kaprekar Number Wikipedia, Kaprekar number Index entries for Colombian or self numbers and related sequences EXAMPLE 703 is Kaprekar because 703 = 494 + 209, 703^2 = 494209. 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. CROSSREFS Cf. A006886, A037042, A053394, A053395, A053396, A053397, A003052, A248353. Sequence in context: A006886 A053816 A290449 * A044492 A207359 A243090 Adjacent sequences: A045910 A045911 A045912 * A045914 A045915 A045916 KEYWORD nonn,base,easy AUTHOR N. J. A. Sloane EXTENSIONS More terms from Michel ten Voorde, Apr 13 2001 Definition clarified by Reinhard Zumkeller, Oct 05 2014 Definition modified and terms corrected by Max Alekseyev, Aug 06 2017 STATUS approved

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Last modified September 13 03:33 EDT 2024. Contains 375857 sequences. (Running on oeis4.)