A341737 a(n) is the number of segments necessary to represent n in the Cistercian numeral system.

1, 2, 2, 2, 2, 3, 2, 3, 3, 4, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 2, 3, 2, 3, 3, 4, 3, 4, 3, 4, 2, 3, 3, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 3, 3, 4, 3, 4, 4, 5, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 2, 3, 3, 3, 3, 4, 3, 4, 4, 5, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 3, 4, 3, 4, 4, 5, 4

Offset: 0

Author

Stefano Spezia, Feb 18 2021

Keywords

• nonn
• base
• fini
• full

Comments

The sequence is finite because the numeral system of Cistercian monks allows us to represent the numbers from 0 to 9999.

Links

• Stefano Spezia, Table of n, a(n) for n = 0..9999
• 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

Crossrefs

Cf. A002963, A092196, A119281.

Programs

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}; 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}]
(* Function for visualizing a Cistercian numeral *)
CistercianNumeral[n_]:=ResourceFunction["CistercianNumberEncode"][n];

Formula

a(n) <= 9.