He sleeps half of it, and stands (in prayer) a third of it, and sleeps a sixth of it. And he would fast one day and break his fast one day."(1)

68 - Chapter: On fasting three days of every month

2449 - Muhammad ibn Kathir narrated to us, Hammad informed us, from Anas, the brother of Muhammad, from Ibn Milhan al-Qaysi, from his father, who said: The Messenger of Allah, peace and blessings be upon him, used to command us to fast the white days: the thirteenth, fourteenth, and fifteenth. He said: And he said: "They are like the passing of all time."(2)

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(1) Its chain is authentic. Muhammad ibn Isa: he is Ibn Najih al-Baghdadi, and Musaddad: he is Ibn Musarhad al-Asadi, and Sufyan: he is Ibn Uyaynah, and Amr: he is Ibn Dinar al-Makki.
It was also recorded by al-Bukhari (1131) and (3420), Muslim (1159), Ibn Majah (1712), and al-Nasa'i in "al-Kubra" (1329) and (2665) via multiple paths from Sufyan ibn Uyaynah, and Muslim (1159) via the path of Ibn Jurayj, both from Amr ibn Dinar, with this chain. It was also recorded by al-Bukhari (1153) and (1974-1980) and (3418-3420) and (5052) and (6134) and (6277), Muslim (1159), al-Tirmidhi (780), and al-Nasa'i (2709-2724) via multiple paths from Abdullah ibn Amr ibn al-As.
They all confined their narrations to mentioning David's fasting without his prayer, and in their view this hadith is part of a story concerning Abdullah ibn Amr himself.
It is in "Musnad Ahmad" (6491), and "Sahih Ibn Hibban" (2590).
See what preceded under numbers (2425) and (2427).

(2) An authentic hadith due to corroborating evidence, and this chain is weak due to the unknown status of Ibn Milhan al-Qaysi — he is Abd al-Malik ibn Qatadah. Muhammad ibn Kathir: he is al-Abdi, and Hammam: he is Ibn Yahya al-Awadhi, and Anas: he is Ibn Sirin al-Ansari.
It was also recorded by Ibn Majah (1707 m), and al-Nasa'i in "al-Kubra" (2752) via the path of Hammam, with this chain. Al-Nasa'i's narration is without his saying: "They are like the passing of all time." =