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

%I A344939 #34 Oct 18 2023 11:35:36
%S A344939 0,1,2,3,10,11,12,20,21,22,100,101,102,103,110,111,112,120,121,122,
%T A344939 200,201,202,210,211,212,213,220,221,222,300,301,1000,1001,1002,1010,
%U A344939 1011,1012,1020,1021,1022,1100,1101,1102,1103,1110,1111,1112,1120,1121,1122
%N A344939 The part of n left of the radix point when written in base Pi using a greedy algorithm representation.
%H A344939 Paolo Xausa, <a href="/A344939/b344939.txt">Table of n, a(n) for n = 0..10000</a>
%H A344939 Wikipedia, <a href="https://en.wikipedia.org/wiki/Non-integer_base_of_numeration">Non-integer base of numeration</a>.
%e A344939 a(5) = 11 because 5 in base Pi is 11.22012202...
%p A344939 A344939 := proc(n)
%p A344939     local e,ntrunc,a,d;
%p A344939     Digits := 1000 ;
%p A344939     if n = 0 then
%p A344939         return 0 ;
%p A344939     end if;
%p A344939     ntrunc := n ;
%p A344939     e := floor(log(n)/log(Pi)) ;
%p A344939     a := 0 ;
%p A344939     while e >= 0 do
%p A344939         d := floor(ntrunc/Pi^e) ;
%p A344939         a := 10*a+d ;
%p A344939         ntrunc := evalf(ntrunc-d*Pi^e) ;
%p A344939         e := e-1 ;
%p A344939     end do:
%p A344939     a ;
%p A344939 end proc:
%p A344939 seq(A344939(n),n=0..15) ; # _R. J. Mathar_, Aug 16 2021
%t A344939 A344939[n_]:=FromDigits[First[RealDigits[n,Pi,Floor[Log[Pi,Max[n,1]]]+1]]];
%t A344939 Array[A344939,100,0] (* _Paolo Xausa_, Oct 17 2023 *)
%Y A344939 Cf. A000796 (Pi digits). Subsequence of A007090.
%Y A344939 Cf. A105116 (base e), A105424 (base phi).
%Y A344939 Cf. A366721 (number of digits).
%K A344939 nonn,base
%O A344939 0,3
%A A344939 _Paolo Xausa_, Jun 03 2021
%E A344939 Name edited by _Paolo Xausa_, Oct 18 2023