Today is D.R. Kaprekar’s 114th birth anniversary.

Kaprekar was an Indian recreational mathematician who described several classes of natural numbers including the Kaprekar, Harshad and Self numbers and discovered the Kaprekar constant, named after him.

Kaprekar numbers are numbers whose square in that base can be split into 2 parts that add up to the original number Here are more such numbers:

9²=81→8+1=9

45²=2025→20+25=45

55²=3025→30+25=55

99²=9801→98+01=99

297²=88209→88+209=297

703²=494209→494+209=703

999²=998001→998+001=999

2223²=4941729→494+1729=2223

Despite having no formal postgraduate training and working as a schoolteacher, Kaprekar published extensively and became well known in recreational mathematics circles.

Kaprekar studied at the Fergusson College in Pune, and was based in Nashik.  Here is an interesting article about link between Kaprekar Constant and music.

The Mystery and Music of Kaprekar Constant – 6174

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