A344939 The part of n left of the radix point when written in base Pi using a greedy algorithm representation.

0, 1, 2, 3, 10, 11, 12, 20, 21, 22, 100, 101, 102, 103, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 213, 220, 221, 222, 300, 301, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022, 1100, 1101, 1102, 1103, 1110, 1111, 1112, 1120, 1121, 1122

Offset: 0

Author

Paolo Xausa, Jun 03 2021

Keywords

• nonn
• base

Examples

			a(5) = 11 because 5 in base Pi is 11.22012202...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Wikipedia, Non-integer base of numeration.

Crossrefs

Cf. A000796 (Pi digits). Subsequence of A007090.

Cf. A105116 (base e), A105424 (base phi).

Cf. A366721 (number of digits).

Programs

Maple

A344939 := proc(n)
    local e,ntrunc,a,d;
    Digits := 1000 ;
    if n = 0 then
        return 0 ;
    end if;
    ntrunc := n ;
    e := floor(log(n)/log(Pi)) ;
    a := 0 ;
    while e >= 0 do
        d := floor(ntrunc/Pi^e) ;
        a := 10*a+d ;
        ntrunc := evalf(ntrunc-d*Pi^e) ;
        e := e-1 ;
    end do:
    a ;
end proc:
seq(A344939(n),n=0..15) ; # R. J. Mathar, Aug 16 2021

Mathematica

A344939[n_]:=FromDigits[First[RealDigits[n,Pi,Floor[Log[Pi,Max[n,1]]]+1]]];
Array[A344939,100,0] (* Paolo Xausa, Oct 17 2023 *)

Extensions

Name edited by Paolo Xausa, Oct 18 2023