OFFSET
1,2
COMMENTS
The sequence is finite because the numeral system of Cistercian monks allows us to represent the numbers from 0 to 9999.
LINKS
Daniel Carter Beard, The American boys' book of signs, signals and symbols. New York Public Library. Philadelphia: Lippincott. p. 92, 1918.
dCode, Cistercian Monk Numerals
Lauron William De Laurence, The Great Book of Magical Art, Hindu Magic and East Indian Occultism. Chicago: De Laurence Co. p. 174, 1915.
Agrippa von Nettesheim and Heinrich Cornelius, De Occulta Philosophia, pp. CXLII - CXLIII, 1533 (in Latin).
Wikipedia, Cistercian numerals.
FORMULA
Sum_{k=1..9} a(k) = 10^4.
MATHEMATICA
SN:={"0"->1, "1"->2, "2"->2, "3"->2, "4"->2, "5"->3, "6"->2, "7"->3, "8"->3, "9"->4}; OI:={11, 15, 17, 19, 22, 28, 29, 51, 55, 57, 59, 71, 75, 77, 79, 82, 88, 89, 91, 92, 95, 97, 98, 99}; a[k_]:=Count[Table[(Characters[IntegerString[Floor[n/100]]]/. SN//Total)-Length[Characters[IntegerString[Floor[n/100]]]]+1-If[MemberQ[OI, Floor[n/100]], 1, 0]-Boole[Floor[n/100]==99]+(Characters[IntegerString[Mod[n, 100]]]/. SN//Total)-Length[Characters[IntegerString[Mod[n, 100]]]]+1-If[MemberQ[OI, Mod[n, 100]], 1, 0]-Boole[Mod[n, 100]==99]-1, {n, 0, 9999}], k]; Array[a, 9]
CROSSREFS
KEYWORD
nonn,base,fini,full,new
AUTHOR
Stefano Spezia, Feb 20 2025
STATUS
approved