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A381788 Greedy expansion of Pi-3 in a base with place values 1/(10^k-1), k >= 1, using digits {0,1,2,...,8,9,A=10}.

%I A381788 #32 Mar 18 2025 14:43:07
%S A381788 1,3,0,1,7,8,5,0,1,4,6,6,5,9,4,7,1,5,1,9,5,6,1,3,4,8,9,3,4,2,2,7,5,2,
%T A381788 2,9,0,3,8,6,2,8,1,1,5,8,3,5,3,1,1,9,8,2,3,5,2,0,8,9,4,1,8,2,4,8,6,3,
%U A381788 1,2,5,9,1,2,9,1,5,5,5,0,6,9,6,8,0,7,7,9,7,4,0,9,8,2,8,5,7,4,1,9,5,5,7,5,2,8,3,1,1,0,8,8,5
%N A381788 Greedy expansion of Pi-3 in a base with place values 1/(10^k-1), k >= 1, using digits {0,1,2,...,8,9,A=10}.
%C A381788 From _Pontus von Brömssen_, Mar 13 2025: (Start)
%C A381788 Since the ratio of successive place values is less than 1/10, a digit A=10 is sometimes needed. For example, if 10*A073668-37/33 < x < 1/9, the expansion of x must have an A at the second position after the radix point (for any choice of digits, not only greedy).
%C A381788 The expansion is not unique without specifying greedy choice of digits. For example, the number 11/1000 can be represented both as 0.010898908982... and (non-greedily) as 0.00A989899171... in this system.
%C A381788 For a random number, the probability that the digit A occurs decreases exponentially with the position in the expansion (with greedy choice of digits), so it seems very unlikely that 10 is a term of this sequence.
%C A381788 (End)
%F A381788 Sum_{k>=1} a(k)/(10^k - 1) = Pi - 3.
%p A381788 BASEN:= proc(x, b, sgn, k)
%p A381788 local i, j, v, premier, fin, lll, liste, w, baz;
%p A381788     baz := evalf(b);
%p A381788     v := abs(frac(evalf(x)));
%p A381788     fin := trunc(evalf(Digits/log10(b)));
%p A381788     lll := [seq(i^k*(baz^i + sgn), i = 1 .. fin)];
%p A381788     liste := [];
%p A381788     for i to fin do w := trunc(v*lll[i]); v := v - w/lll[i]; liste := [op(liste), w] end do;
%p A381788     RETURN(liste)
%p A381788 end;
%p A381788 BASEN(Pi-3,10,-1,0);
%Y A381788 Cf. A000796, A073668.
%K A381788 nonn,base
%O A381788 1,2
%A A381788 _Simon Plouffe_, Mar 07 2025
%E A381788 Edited by _N. J. A. Sloane_, Mar 18 2025