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%I #38 Nov 21 2019 04:39:44
%S 10,12,13,14,15,16,17,18,19,20,23,24,25,26,27,28,29,30,34,35,36,37,38,
%T 39,40,45,46,47,48,49,50,56,57,58,59,60,67,68,69,70,78,79,80,89,90,
%U 102,103,104,105,106,107,108,109,112,113,114,115,116,117,118,119,123
%N "True so far" sequence: floor(a(n)/10) is the number of digits (a(n) mod 10) within the first n terms; a(n) is the smallest such number larger than a(n-1).
%C Original definition (edited): In a(n), the last digit must be seen as a glyph and preceding digits as a number, counting occurrences of the glyph up to and including a(n). "10" reads [one '0'] and "12" [one '2'] - which are both true statements: there is one '0' glyph so far in the sequence when 10 is read and there is one '2' glyph when 12 is read. The sequence is built with a(n+1)-a(n) being minimal, positive, and a(n) always "true so far". This explains why there are no integers 11, 21, 22, 31 etc.: their statements are false.
%C Terms must increase. Without this condition we obtain A102850. - _David Wasserman_, Feb 13 2008
%C The substring ...1112,1113,1114,1115,1116,1117... appears in the sequence - which means that so far the whole sequence has used 111 '2's, 111 '3's, 111 '4's, 111 '5's, 111 '6's and 111 '7's. [Corrected (1118 is not in the sequence!) by _M. F. Hasler_, Nov 18 2019]
%C The sequence is finite. The last term is a(2024) = 8945. The largest terms ending with each digit appear to be: 5890, 8201, 8312, 8623, 8734, 8945, 7756, 6697, 6778, 5979. - Chuck Seggelin, Feb 22, 2005 [Corrected '8495' but other terms unverified. - _M. F. Hasler_, Nov 18 2019]
%C When this sequence terminates there are 624 zero, 822 ones, 834 twos, 864 threes, 874 fours, 894 fives, 779 sixes, 697 sevens, 697 eights and 617 nines. - _Robert G. Wilson v_, Feb 22(?) 2005
%H Nathaniel Johnston, <a href="/A102357/b102357.txt">Table of n, a(n) for n = 1..2024</a> (based on C. Seggelin's data)
%H Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/TrueSoSol.htm">Sequence True-so-far</a>
%H Eric Angelini, <a href="/A102357/a102357.pdf">Sequence True-so-far</a> [Cached copy with permission]
%H C. Seggelin, <a href="/A102357/a102357.htm">Sequence True-So-Far</a>
%t 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}] (* _Robert G. Wilson v_, Feb 22 2005 *)
%o (PARI) c=Vec(0, 10); a=10; for(n=1, 2024, while(a\10<=c[a%10+1] || a\10 != c[a%10+1]+#select(d->d==a%10, digits(a)), a++); [c[d+1]++|d<-digits(a)]; print1(a",")) \\ _M. F. Hasler_, Nov 18 2019
%Y Cf. A102850.
%K base,easy,nonn,fini,full
%O 1,1
%A _Eric Angelini_, Feb 21 2005
%E Chuck Seggelin and _David W. Wilson_ both computed the full 2024 terms
%E Offset corrected by _Nathaniel Johnston_, May 17 2011
%E Edited and shorter definition from _M. F. Hasler_, Nov 18 2019
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