True So Far

[Chuck Seggelin]

Hi Eric,

The last term in the sequence appears to be 8945, with a total of 2024 terms 
(tested to a(2000000)).

Of course there may be errors in my code, but I think I got it right.  I 
didn't get exactly the same results you did though, for example 1118 does 
not appear in my output.

You can look at the output here:

http://unbecominglevity.blogharbor.com/supplements/tsf_output.txt

And the VB code used to generate it here:

http://unbecominglevity.blogharbor.com/supplements/tsf_vb_code.txt

The output is divided into 3 sections, the first is just a list of all the 
terms, the second is the final counts for each digit, and the third is 
"Eric's format"--the list of terms again which I attempted to format in the 
same way you did.

A note on the "final values for each digit" section of the output: these are 
the counts of the number of times each digit appeared in the sequence, *not* 
the last term which ended with that digit.  For example the last term ending 
in 0 was 5890, but other subsequent terms included 0 (for example 6008), so 
the count for any digit keeps going up until the last term of the sequence 
is found.

The largest terms ending with each digit appear to be:

5890, 8201, 8312, 8623, 8734, 8495, 7756, 6697, 6778, 5979

                                -- Chuck Seggelin

----- Original Message ----- 
From: "Eric Angelini" <keynews.tv at skynet.be>
To: "math-fun" <math-fun at mailman.xmission.com>; <seqfan at ext.jussieu.fr>
Sent: Tuesday, February 22, 2005 6:26 AM
Subject: True So Far


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.