Katapayadi sankhya is a simplification of Aryabhata's Sanskrit numerals, due probably to Haridatta from Kerala. In Malayalam it is also known as 'Paralperu'

For eg: ചണ്ഡാംശുചന്ദ്രാധമകുംഭിപാല
represents 31415926536 which is π*1000000000000000

More examples in Malayalam are given in this page

The Katapayadi sankhya is a way of determining the number of a Melakarta raga from the first two syllables of the name of the Raga.

The algorithm used in this is explained in detail here: An Algorithm to derive the Swarasthanas