Beside the phonetic order there is a second Buddhist arrangement of syllables entirely, the arapacana, named from its opening five: a, ra, pa, ca, na. It runs to forty-two syllables and it is not ordered by articulation at all. Its sequence is generally thought to reflect the order of the Kharosthi script, which was used in the northwest of the subcontinent and in Central Asia and which is unrelated to the Brahmi family in its letterforms.
Its function in the texts is mnemonic. Each syllable heads a doctrinal statement, so the sequence of syllables carries a sequence of teachings, and reciting the list recalls the whole set. Arrangements of that kind appear in several Mahayana works, and the arapacana is associated in particular with Manjushri, who is invoked in a form named from it.
Its existence is a useful corrective to the impression the letter tables give. The Indian phonetic order is a description of a sound system; the arapacana is a memory device built on syllables, indifferent to articulation, and derived from a different script tradition. Both circulated in Buddhist literature at the same time and neither displaced the other, because they were doing different jobs. A syllabary is not one kind of object.