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

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Wikipedia, Non-integer base of numeration.

Example

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

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 *)

Crossrefs

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

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

Cf. A366721 (number of digits).

Sequence in context: A212067 A060811 A146327 * A278742 A250174 A285622

Adjacent sequences: A344936 A344937 A344938 * A344940 A344941 A344942

Keyword

nonn,base

Author

Paolo Xausa, Jun 03 2021

Extensions

Name edited by Paolo Xausa, Oct 18 2023

Status

approved