A325479 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.

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, 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, 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

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..129.

Example

0.1234567891011314151617181920212242526272829303132335363738394...

Mathematica

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]
(* To generate terms which include all positive integers up to 200: *)
generate[200]

Crossrefs

Cf. A033307 (Champernowne's constant), A189823 (reduced Champernowne constant).

Sequence in context: A033307 A007376 A189823 * A001073 A274580 A241494

Adjacent sequences: A325476 A325477 A325478 * A325480 A325481 A325482

Keyword

nonn,base,cons,easy

Author

Jonathan P. Shock, Sep 06 2019

Status

approved