True So Far

[Robert G. Wilson v]

Eric, et al,

	Checking what I have seen so far, I saw an error in the terms given. It is
that the entry of 90 was stated twice whereas it should be only stated once.
Other than that this is how I see the sequence. Also checking all the terms I
generated with those at
  http://unbecominglevity.blogharbor.com/supplements/tsf_output.txt agree
perfectly.

Sincerely, Bob.


%I A000001
%S A000001 10,12,13,14,15,16,17,18,19,20,23,24,25,26,27,28,29,30,34,35,36,37,38,
%T A000001 39,40,45,46,47,48,49,50,56,57,58,59,60,67,68,69,70,78,79,80,89,90,102,
%U A000001 103,104,105,106,107,108,109,112,113,114,115,116,117,118,119,123,124
%N A000001 True so far.
%C A000001 "True so far" sequence. Last digit of a(n) must be seen as a glyph and 
preceding digits as a quantity. So "10" reads [one "0"] and "12" [one "2"] -- 
which are both true statements: there is only one "0" glyph so far in the sequence 
when [10] is read, and there is only one "2" glyph when [12] is read. The sequence 
is built with [a(n+1)-a(n)] being minimal and a(n+1) always "true so far". This 
explains why integers [11], [21], [22], [31], etc. are not in: their statements 
are false.
%C A000001 The last entry is a(2024)=8945. - Chuck Seggelin
%C A000001 The largest terms ending with each digit appear to be: 5890, 8201, 
8312, 8623, 8734, 8495, 7756, 6697, 6778, 5979. - Chuck Seggelin.
%C A000001 When this sequence hits the end there are: 624 zero, 822 ones, 834 
twos, 864 threes, 874 fours, 894 fives, 779 sixes, 697 sevens, 697 eights and 617 
nines. - RGWv.
%H A000001 C. Seggelin, <a 
href="http://www.cetteadressecomportecinquantesignes.com/TrueSoFar.htm"> Séquence 
True-so-far</a>.
%H A000001 C. Seggelin, <a 
href="http://unbecominglevity.blogharbor.com/supplements/tsf_output.txt">2024 
terms</a>.
%t A000001 a[0] = {}; a[n_] := a[n] = Block[{k = Max[a[n - 1], 0], b = Sort[ 
Flatten[ Table[ IntegerDigits[ a[i]], {i, 0, n - 1}] ]]}, While[ Count[ Join[b, 
IntegerDigits[ IntegerPart[k/10]]], Mod[k, 10]] != IntegerPart[k/10], k++ ]; k]; 
Table[ a[n], {n, 63}] (from RGWv Feb 22 2005)
%Y A000001 Cf. A123456, A123457.
%O A000001 1,1
%K A000001 fini,nonn,word
%A A000001 Eric Angelini (eric.angelini at skynet.be),  Feb 22 2005

Eric Angelini wrote:

> Hello math-fun and seqfan,
> 
> I've just sent this to the OEIS :
> 
>     10 12 13 14 15 16 17 18 19 20 23 24 25 26 27 28 29 30
>     34 35 36 37 38 39 40 45 46 47 48 49 50 56 57 58 59 60
>     67 68 69 70 78 79 80 89 90 90 102 103 104 105 106 107
>     108 109 112 113 114 115 116 117 118 119 123 124 125
>     126 127 128 129 134 135 136 137 138 139 145 146 147
>     148 149 156 157 158 159 167 168 169 178 179 180 189...
> 
> [more hand calculated terms here (hope no errors)]:
> 
> http://www.cetteadressecomportecinquantesignes.com/TrueSoFar.htm
> 
> Description :
> 
>     "True so far"-sequence. Last digit of a(n) must be seen
>     as a glyph and preceding digits as a quantity. So "10"
>     reads [one "0"] and "12" [one "2"] -- which are both true
>     statements: there is only one "0" glyph so far in the
>     sequence when [10] is read, and there is only one "2"
>     glyph when [12] is read. The sequence is built with
>     [a(n+1)-a(n)] being minimal and a(n+1) always "true so
>     far". This explains why integers [11], [21], [22], [31],
>     etc. are not in: their statements are false.
> 
>     The nice substring ...1112,1113,1114,1115,1116,1117 1118...
>     appears in the sequence -- which means that so far the
>     whole sequence has used 111 "2", 111 "3", 111 "4", 111 "5",
>     111 "6", 111 "7" and 111 "8"...
> 
> Question which ruined my sleep tonight:
> 
> « Will the sequence ever stop? »
> 
> ... my intuition says yes...
> ... could someone compute this and check for some more integers?
> 
> Thanks,
> É.