

A102357


"True so far" sequence. Last digit of a(n) must be seen as a glyph and preceding digits as a number. 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 there are no integers [11], [21], [22], [31] etc.: their statements are false.


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

Terms must increase. Without this condition we obtain A102850.  David Wasserman, Feb 13 2008
The 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"...
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, 8495, 7756, 6697, 6778, 5979.  Chuck Seggelin
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


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 *)


CROSSREFS

Cf. A102850.
Sequence in context: A043638 A280824 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


STATUS

approved



