APOD and General Astronomy Discussion Forum
https://asterisk.apod.com/
https://en.wikipedia.org/wiki/D._R._Kaprekar wrote:
<<Dattatreya Ramchandra Kaprekar (1905–1986) was an Indian recreational mathematician who described several classes of natural numbers including the Kaprekar, harshad and self numbers and discovered the Kaprekar's constant, named after him. Despite having no formal postgraduate training and working as a schoolteacher, he published extensively and became well known in recreational mathematics circles.
A Kaprekar number is a positive integer with the property that if it is squared, then its representation can be partitioned into two positive integer parts whose sum is equal to the original number (e.g. 45, since 452=2025, and 20+25=45, also 9, 55, 99 etc.)
Some examples of Kaprekar numbers in base 10,
are (sequence A006886 in the OEIS):
Code: Select all
Number Square Decomposition ................................................. 703 703² = 494209 494+209 = 703 2728 2728² = 7441984 744+1984 = 2728 5292 5292² = 28005264 28+005264 = 5292 7777 7777² = 60481729 6048+1729 = 7777
