Based on the search results, there is no specific event or holiday mentioned for October 13, 2023 in India. However, there are two websites that provide information about Panchang, which is a Hindu calendar that provides information about auspicious and inauspicious timings for each day. The Panchang for October 13, 2023 is available on both websites, which provide information about Tithi, Nakshatra, and other details for that day. It is important to note that Panchang timings are represented in local time and may vary depending on the location in India.