User blog:Naruyoko/Values of Rayo's Function for Small Inputs

Input Value Formula 0..6    0      7..23     1 ¬∃a:a∈b 26..51    2 (¬∃a:a∈b)∧b∈c∧¬∃a:a∈c∧¬a=b 52..86    3 (¬∃a:a∈b)∧(¬∃a:a∈c∧¬a=b)∧b∈c∈d∧b∈d∧¬∃a:a=d∧¬a=b∧¬a=c 87..128    4 (¬∃a:a∈b)∧(¬∃a:a∈c∧¬a=b)∧(¬∃a:a∈d∧¬a∈b∧¬a∈c)∧b∈c∈d∈e∧b∈d∧b∈e∧c∈e∧¬∃a:a∈e∧¬a=b∧¬a=c∧¬a=d 129..???    5 (¬∃a:a∈b)∧(¬∃a:a∈c∧¬a=b)∧(¬∃a:a∈d∧¬a∈b∧¬a∈c)∧(¬∃a:a∈e∧¬a=b∧¬a=c∧¬a=d)∧b∈c∈d∈e∈f∧b∈d∈f∧b∈e∧c∈e∧c∈f∧b∈f∧¬∃a:a∈f∧¬a=b∧¬a=c∧¬a=d∧¬a=e Insert Succession Insert Iterated Succession Insert Iterated Iterated Succession Insert Nested Iterated Succession Insert Some Fast Function Insert More Fast Function Insert Unfabonable Function Insert Busy Beaver Function Insert Oracle Busy Beaver Function Insert Functions That is So Fast That No Recursive Analogue of Named Cardinals Can Express It                Insert Madness