A381917 Kaprekar numbers that are the concatenation of two equal numbers.

55, 99, 5050, 7272, 7777, 9999, 500500, 648648, 851851, 999999, 13641364, 24752475, 25252525, 36363636, 50005000, 61116111, 88888888, 99999999, 1111111111, 3888938889, 4132841328, 5000050000, 5243952439, 9756097560, 9999999999, 159341159341, 175676175676, 233415233415

Offset: 1

Author

Shyam Sunder Gupta, Mar 10 2025

Keywords

• base
• nonn

Comments

All repdigit numbers of even length which are Kaprekar numbers are terms. Since 99, 9999, 999999, ... and 5050, 500500, 50005000, ... are Kaprekar numbers, there are infinitely many terms.

Examples

			648648 is a Kaprekar number which is the concatenation of 648 and 648.
		

Links

• Shyam Sunder Gupta, Table of n, a(n) for n = 1..2163
• Shyam Sunder Gupta, On Some Marvellous Numbers of Kaprekar, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 9, 275-315.

Crossrefs

Intersection of A006886 and A020338.

Cf. A092118.