It is well known that articles 'a' and 'an' precede consonant and vowel respectively. But the bone of contention falls in an area where the word starts with 'h'. We tend to silence 'h' most of the time in pronouncing some words that begin with 'h' whereas we could be wrong. I may not be able to put all the words here, but I believe, by my level of competence and performance as a scholar in English language, the words below are the only ones that have silent 'h' in English language. You can prove otherwise all the same. We are all learning.
hour (noun, adverb or when compounded), haute couture/cuisine, heir, heiress, honest (noun, adjective or adverb), Hon (short form of Honourable), honour, Honourable, Honourary, honourarily (any word beginning with 'honour')
Each of these words takes the article 'an' while all other words in English beginning with 'h' take article 'a' depending on what determiner they represent. (Don't forget we have other determiners).
"an hour, an honour, a helicopter, a haircut, a house, a hotel, an honest"