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@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, Ã.