

A102357


"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(n1).


14



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, 102, 103, 104, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 118, 119, 123
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OFFSET

1,1


COMMENTS

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.
Terms must increase. Without this condition we obtain A102850.  David Wasserman, Feb 13 2008
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]
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]
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


LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..2024 (based on C. Seggelin's data)
Eric Angelini, Sequence Truesofar
Eric Angelini, Sequence Truesofar [Cached copy with permission]
C. Seggelin, Sequence TrueSoFar


MATHEMATICA

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 *)


PROG

(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


CROSSREFS

Cf. A102850.
Sequence in context: A280824 A329448 A261907 * A102850 A043493 A105959
Adjacent sequences: A102354 A102355 A102356 * A102358 A102359 A102360


KEYWORD

base,easy,nonn,fini,full


AUTHOR

Eric Angelini, Feb 21 2005


EXTENSIONS

Chuck Seggelin and David W. Wilson both computed the full 2024 terms
Offset corrected by Nathaniel Johnston, May 17 2011
Edited and shorter definition from M. F. Hasler, Nov 18 2019


STATUS

approved



