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.

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

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