Question: Who is Hrólfr Gautreksson's paternal grandfather?

Knowledge 1: Hrólfr Gautreksson
Hrólfr Gautreksson was a legendary Geatish king who appears in "Hrólfs saga Gautrekssonar" and probably in "Hyndluljóð"."Hrólfs saga Gautrekssonar" tells that he was the son of king Gautrek and when his father died, his elder brother Ketill became king.Hrólfr would court and finally win the Swedish king Erik's daughter Þornbjörg, who was a violent and proud transmasculine king.He later succeeded his brother as king.There is also an isolated stanza in "Hyndluljóð" where Hrólfr the Old appears.The names Þorir the Iron-Shield and Grímr shows that the lines probably refer to Þorir and Grímr Þorkelsson who appear with Hrólfr in "Hrólfs saga Gautrekssonar".Translations: "Hrolf Gautreksson, a Viking romance".Translated by Hermann Pálsson, Paul Geoffrey Edwards.University of Toronto Press, 1972.148 pages. [SEP] Knowledge 2: Gautrekr
Gautrekr was a legendary Geatish king who appears in several sources, such as "Gautreks sagaHrólfs saga GautrekssonarBósa saga ok HerrauðsYnglinga sagaNafnaþulur" (part of the "Prose Edda") and "Af Upplendinga konungum".He appears in different temporal settings, and he could represent different kings named Gautrekr, as the name simply means "Geatish ruler".In the various settings, he also has different offspring.However, all settings present him as the son of a Gaut or Gauti, and in one of the later settings, his father Gaut gave his name to Götaland (Geatland).In "Nafnaþulur", he is mentioned as one of the sea-kings, after his father Gauti.
Knowledge 1: Hrólfr Gautreksson
Hrólfr Gautreksson was a legendary Geatish king who appears in "Hrólfs saga Gautrekssonar" and probably in "Hyndluljóð"."Hrólfs saga Gautrekssonar" tells that he was the son of king Gautrek and when his father died, his elder brother Ketill became king.Hrólfr would court and finally win the Swedish king Erik's daughter Þornbjörg, who was a violent and proud transmasculine king.He later succeeded his brother as king.There is also an isolated stanza in "Hyndluljóð" where Hrólfr the Old appears.The names Þorir the Iron-Shield and Grímr shows that the lines probably refer to Þorir and Grímr Þorkelsson who appear with Hrólfr in "Hrólfs saga Gautrekssonar".Translations: "Hrolf Gautreksson, a Viking romance".Translated by Hermann Pálsson, Paul Geoffrey Edwards.University of Toronto Press, 1972.148 pages. [SEP] Knowledge 2: Fujiwara no Nagara
, also known as Fujiwara no Nagayoshi, was a Japanese statesman, courtier and politician of the early Heian period.He was the grandfather of Emperor Yōzei.
Knowledge 1: Hrólfr Gautreksson
Hrólfr Gautreksson was a legendary Geatish king who appears in "Hrólfs saga Gautrekssonar" and probably in "Hyndluljóð"."Hrólfs saga Gautrekssonar" tells that he was the son of king Gautrek and when his father died, his elder brother Ketill became king.Hrólfr would court and finally win the Swedish king Erik's daughter Þornbjörg, who was a violent and proud transmasculine king.He later succeeded his brother as king.There is also an isolated stanza in "Hyndluljóð" where Hrólfr the Old appears.The names Þorir the Iron-Shield and Grímr shows that the lines probably refer to Þorir and Grímr Þorkelsson who appear with Hrólfr in "Hrólfs saga Gautrekssonar".Translations: "Hrolf Gautreksson, a Viking romance".Translated by Hermann Pálsson, Paul Geoffrey Edwards.University of Toronto Press, 1972.148 pages. [SEP] Knowledge 2: Kaya Alp
Kaya Alp was, according to Ottoman tradition, the son of Kızıl Buğa and the father of Suleyman Shah, who was, in turn, the grandfather of Ertuğrul, and the great grandfather of the Ottoman Empire founder, Osman I.

Answer: Gaut