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

0,2

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

Formula

a(n) <= 9.

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];

Crossrefs

Cf. A002963, A092196, A119281.

Sequence in context: A086833 A010764 A029383 * A351033 A318837 A070098

Adjacent sequences: A341734 A341735 A341736 * A341738 A341739 A341740

Keyword

nonn,base,fini,full

Author

Stefano Spezia, Feb 18 2021

Status

approved