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The hexaelgathor regiment is a series of numbers from E100(#^#^#^6)100 to E100(#^#^#^7)90 defined using Cascading-E notation (i.e. beginning from hexaelgathor and up to hexaelgathornonagintice).[1] The numbers were coined by Sbiis Saibian.

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## List of numbers of the regiment

 Name of number Cascading-E notation (definition) Fast-growing hierarchy (approximation) Hexaelgathor E100#^#^######100 = E100(#^#^#^6)100 $$f_{\omega^{\omega^{\omega^6}}}(100)$$ Grand hexaelgathor E100(#^#^#^6)hexaelgathor $$f_{\omega^{\omega^{\omega^6}}}^2(100)$$ Grangol-carta-hexaelgathor E100(#^#^#^6)100#100 $$f_{\omega^{\omega^{\omega^6}}+1}(100)$$ Godgahlah-carta-hexaelgathor E100(#^#^#^6)100#^#100 $$f_{\omega^{\omega^{\omega^6}}+\omega^\omega}(100)$$ Godgathor-carta-hexaelgathor E100(#^#^#^6)100#^#^#100 $$f_{\omega^{\omega^{\omega^6}}+\omega^{\omega^\omega}}(100)$$ Gralgathor-carta-hexaelgathor E100(#^#^#^6)100#^#^##100 $$f_{\omega^{\omega^{\omega^6}}+\omega^{\omega^{\omega^2}}}(100)$$ Thraelgathor-carta-hexaelgathor E100(#^#^#^6)100#^#^###100 $$f_{\omega^{\omega^{\omega^6}}+\omega^{\omega^{\omega^3}}}(100)$$ Terinngathor-carta-hexaelgathor E100(#^#^#^6)100#^#^####100 $$f_{\omega^{\omega^{\omega^6}}+\omega^{\omega^{\omega^4}}}(100)$$ Pentaelgathor-carta-hexaelgathor E100(#^#^#^6)100(#^#^#^5)100 $$f_{\omega^{\omega^{\omega^6}}+\omega^{\omega^{\omega^5}}}(100)$$ Hexaeltrigathor E100(#^#^#^6)100(#^#^#^6)100 $$f_{\omega^{\omega^{\omega^6}}2}(100)$$ Hexaeltergathor E100(#^#^#^6)100(#^#^#^6)100(#^#^#^6)100 = E100(#^#^#^6)*#4 $$f_{\omega^{\omega^{\omega^6}}3}(100)$$ Hexaelpeggathor E100(#^#^#^6)*#5 $$f_{\omega^{\omega^{\omega^6}}4}(100)$$ Hexaelhexgathor E100(#^#^#^6)*#6 $$f_{\omega^{\omega^{\omega^6}}5}(100)$$ Hexaelhepgathor E100(#^#^#^6)*#7 $$f_{\omega^{\omega^{\omega^6}}6}(100)$$ Hexael-ahtgathor E100(#^#^#^6)*#8 $$f_{\omega^{\omega^{\omega^6}}7}(100)$$ Hexael-enngathor E100(#^#^#^6)*#9 $$f_{\omega^{\omega^{\omega^6}}8}(100)$$ Hexaeldekagathor E100(#^#^#^6)*#10 $$f_{\omega^{\omega^{\omega^6}}9}(100)$$ Hexaelgathor-by-hyperion E100(#^#^#^6)*#100 $$f_{\omega^{\omega^{\omega^6}+1}}(100)$$ Hexaelgathor-by-godgahlah E100(#^#^#^6)*#^#100 $$f_{\omega^{\omega^{\omega^6}+\omega}}(100)$$ Hexaelgathor-by-godgathor E100(#^#^#^6)*#^#^#100 $$f_{\omega^{\omega^{\omega^6}+\omega^\omega}}(100)$$ Hexaelgathor-by-gralgathor E100(#^#^#^6)*#^#^##100 $$f_{\omega^{\omega^{\omega^6}+\omega^{\omega^2}}}(100)$$ Hexaelgathor-by-thraelgathor E100(#^#^#^6)*#^#^###100 $$f_{\omega^{\omega^{\omega^6}+\omega^{\omega^3}}}(100)$$ Hexaelgathor-by-terinngathor E100(#^#^#^6)*#^#^####100 $$f_{\omega^{\omega^{\omega^6}+\omega^{\omega^4}}}(100)$$ Hexaelgathor-by-pentaelgathor E100(#^#^#^6)*(#^#^#^5)100 $$f_{\omega^{\omega^{\omega^6}+\omega^{\omega^5}}}(100)$$ Deutero-hexaelgathor E100(#^#^#^6)*(#^#^#^6)100 $$f_{\omega^{\omega^{\omega^6}2}}(100)$$ Trito-hexaelgathor E100(#^#^#^6)*(#^#^#^6)*(#^#^#^6)100 $$f_{\omega^{\omega^{\omega^6}3}}(100)$$ Teterto-hexaelgathor E100(#^#^#^6)*(#^#^#^6)*(#^#^#^6)*(#^#^#^6)100 = E100#^(#^#^6*#)4 $$f_{\omega^{\omega^{\omega^6}4}}(100)$$ Pepto-hexaelgathor E100#^(#^#^6*#)5 $$f_{\omega^{\omega^{\omega^6}5}}(100)$$ Exto-hexaelgathor E100#^(#^#^6*#)6 $$f_{\omega^{\omega^{\omega^6}6}}(100)$$ Epto-hexaelgathor E100#^(#^#^6*#)7 $$f_{\omega^{\omega^{\omega^6}7}}(100)$$ Ogdo-hexaelgathor E100#^(#^#^6*#)8 $$f_{\omega^{\omega^{\omega^6}8}}(100)$$ Ento-hexaelgathor E100#^(#^#^6*#)9 $$f_{\omega^{\omega^{\omega^6}9}}(100)$$ Dekato-hexaelgathor E100#^(#^#^6*#)10 $$f_{\omega^{\omega^{\omega^6}10}}(100)$$ Isosto-hexaelgathor E100#^(#^#^6*#)20 $$f_{\omega^{\omega^{\omega^6}20}}(100)$$ Trianto-hexaelgathor E100#^(#^#^6*#)30 $$f_{\omega^{\omega^{\omega^6}30}}(100)$$ Saranto-hexaelgathor E100#^(#^#^6*#)40 $$f_{\omega^{\omega^{\omega^6}40}}(100)$$ Peninto-hexaelgathor E100#^(#^#^6*#)50 $$f_{\omega^{\omega^{\omega^6}50}}(100)$$ Exinto-hexaelgathor E100#^(#^#^6*#)60 $$f_{\omega^{\omega^{\omega^6}60}}(100)$$ Ebdominto-hexaelgathor E100#^(#^#^6*#)70 $$f_{\omega^{\omega^{\omega^6}70}}(100)$$ Ogdonto-hexaelgathor E100#^(#^#^6*#)80 $$f_{\omega^{\omega^{\omega^6}80}}(100)$$ Eneninto-hexaelgathor E100#^(#^#^6*#)90 $$f_{\omega^{\omega^{\omega^6}90}}(100)$$ Hecato-hexaelgathor E100#^(#^#^6*#)100 $$f_{\omega^{\omega^{\omega^6+1}}}(100)$$ Hexaelgridgathor E100#^(#^#^6*##)100 $$f_{\omega^{\omega^{\omega^6+2}}}(100)$$ Hexaelkubikgathor E100#^(#^#^6*###)100 $$f_{\omega^{\omega^{\omega^6+3}}}(100)$$ Hexaelquarticgathor E100#^(#^#^6*####)100 $$f_{\omega^{\omega^{\omega^6+4}}}(100)$$ Hexaelgodgathgathor E100#^(#^#^6*#^#)100 $$f_{\omega^{\omega^{\omega^6+\omega}}}(100)$$ Hexaelgralgathgathor E100#^(#^#^6*#^##)100 $$f_{\omega^{\omega^{\omega^6+\omega^2}}}(100)$$ Hexaelthraelgathgathor E100#^(#^#^6*#^###)100 $$f_{\omega^{\omega^{\omega^6+\omega^3}}}(100)$$ Hexaelterinngathgathor E100#^(#^#^6*#^####)100 $$f_{\omega^{\omega^{\omega^6+\omega^4}}}(100)$$ Hexaelpentaelgathgathor E100#^(#^#^6*#^#^5)100 $$f_{\omega^{\omega^{\omega^6+\omega^5}}}(100)$$ Hexaelgathordeus E100#^(#^#^6*#^#^6)100 $$f_{\omega^{\omega^{\omega^62}}}(100)$$ Hexaelgathortruce E100#^(#^#^6*#^#^6*#^#^6)100 $$f_{\omega^{\omega^{\omega^63}}}(100)$$ Hexaelgathorquad E100#^(#^#^6*#^#^6*#^#^6*#^#^6)100 = E100(#^#^#^7)4 $$f_{\omega^{\omega^{\omega^64}}}(100)$$ Hexaelgathorquid E100(#^#^#^7)5 $$f_{\omega^{\omega^{\omega^65}}}(100)$$ Hexaelgathorsid E100(#^#^#^7)6 $$f_{\omega^{\omega^{\omega^66}}}(100)$$ Hexaelgathorseptuce E100(#^#^#^7)7 $$f_{\omega^{\omega^{\omega^67}}}(100)$$ Hexaelgathoroctuce E100(#^#^#^7)8 $$f_{\omega^{\omega^{\omega^68}}}(100)$$ Hexaelgathornonice E100(#^#^#^7)9 $$f_{\omega^{\omega^{\omega^69}}}(100)$$ Hexaelgathordecice E100(#^#^#^7)10 $$f_{\omega^{\omega^{\omega^610}}}(100)$$ Hexaelgathorvigintice E100(#^#^#^7)20 $$f_{\omega^{\omega^{\omega^620}}}(100)$$ Hexaelgathortrigintice E100(#^#^#^7)30 $$f_{\omega^{\omega^{\omega^630}}}(100)$$ Hexaelgathorquadragintice E100(#^#^#^7)40 $$f_{\omega^{\omega^{\omega^640}}}(100)$$ Hexaelgathorquinquagintice E100(#^#^#^7)50 $$f_{\omega^{\omega^{\omega^650}}}(100)$$ Hexaelgathorsexagintice E100(#^#^#^7)60 $$f_{\omega^{\omega^{\omega^660}}}(100)$$ Hexaelgathorseptuagintice E100(#^#^#^7)70 $$f_{\omega^{\omega^{\omega^670}}}(100)$$ Hexaelgathoroctogintice E100(#^#^#^7)80 $$f_{\omega^{\omega^{\omega^680}}}(100)$$ Hexaelgathornonagintice E100(#^#^#^7)90 $$f_{\omega^{\omega^{\omega^690}}}(100)$$

## Sources

1. Saibian, Sbiis. Cascading-E Numbers. Retrieved 2017-10-13.