%I #31 Oct 04 2019 13:16:54
%S 1,2,3,4,5,6,7,8,9,1,0,1,1,3,1,4,1,5,1,6,1,7,1,8,1,9,2,0,2,1,2,2,4,2,
%T 5,2,6,2,7,2,8,2,9,3,0,3,2,3,3,5,3,6,3,7,3,8,3,9,4,0,4,3,4,4,6,4,7,4,
%U 8,4,9,5,0,5,4,5,5,7,5,8,5,9,6,0,6,5,6,6,8,6,9,7,0,7,6,7,7,9,8,0,8,7,8,8,9,0,9,9,1,0,0,1,0,2,1,0,3,1,0,4,1,0,5,1,0,6,1,0,7,1
%N Decimal expansion of a normal number in base 10, which, on average, up to any given integer appearance (above 11), is more compact than Champernowne's constant, and more compact than A189823.
%C This number is normal in base 10. On average, any integer above 11 can be found in this decimal expansion at a place earlier than in Champernowne's constant, thus making it a more densely encoded normal number.
%e 0.1234567891011314151617181920212242526272829303132335363738394...
%t isitthere[seq_, n_] := SequencePosition[seq, IntegerDigits[n]]; addtoseq[seq_, n_] := Module[{}, id = IntegerDigits[n]; len = Length[id]; For[i = 1, i < len, i++, If[seq[[i - len;;]] == id[[;; -i - 1]], Return[Join[seq, id[[-i;;]]]]]]; Return[ Join[seq, id]]]; generate[upto_] := Module[{}, start = {1}; For[m = 1, m <= upto, m++, If[isitthere[start, m] === {}, start = addtoseq[start, m]]];start]
%t (* To generate terms which include all positive integers up to 200: *)
%t generate[200]
%Y Cf. A033307 (Champernowne's constant), A189823 (reduced Champernowne constant).
%K nonn,base,cons,easy
%O 0,2
%A _Jonathan P. Shock_, Sep 06 2019