OFFSET
1,2
COMMENTS
"Lexicographically earliest" means in the sense of a sequence of integers, not digits.
S is infinite, of course, as it can always be extended with an integer (not yet present) containing only 1's.
Apart from numbers containing the digit zero, the first numbers that cannot appear as terms are 14, 18, 34, 38, 54, 58, 74, 78, 94, 98, 113, 114, 118, 133, 134, 138, 141, 142, 143, 144, 145, 146, 147, 148, 149, 154, 158, 163, 173, 174, 178, 181, 182, 183, 184, 185, 186, 187, 188, 189, 193, 194, 198, 214, 218, 223, 228, 233, 234, 238, 253, 254, 258, 263, 268, 274, 278, 283, 293, 294, 298, 313, 314, 318, 323, 334, ... - Hans Havermann, Jul 14 2014
REFERENCES
Eric Angelini, Posting to Sequence Fans Mailing List, Jun 26 2014
LINKS
Jean-Marc Falcoz, Table of n, a(n) for n = 1..10009
EXAMPLE
Example:a) draw a line between 6 and 4, for instance -- thus p = 6:
S = 1,2,3,11,5,6|,4,
b) concatenate the last 6 digits before the line (to get Z):
Z = 231156
c) Z/p is an integer (indeed, Z/6 = 38526)
Here are notes on the initial terms:
Z / p = integer (Z ends in p and has digit-length p)
1 / 1 = 1
12 / 2 = 6
123 / 3 = 41
1 / 1 = 1
1 / 1 = 1
23115 / 5 = 4623
231156 / 6 = 38526
1564 / 4 = 391
23115648 / 8 = 2889456
1 / 1 = 1
12 / 2 = 6
1 / 1 = 1
213 / 3 = 71
1 / 1 = 1
21315 / 5 = 4263
52 / 2 = 26
1 / 1 = 1
12 / 2 = 6
22 / 2 = 11
22 / 2 = 11
2224 / 4 = 556
1 / 1 = 1
1222417 / 7 = 174631
1 / 1 = 1
241716 / 6 = 40286
62 / 2 = 31
71625 / 5 = 14325
1 / 1 = 1
417162519 / 9 = 46351391
1625197 / 7 = 232171
72 / 2 = 36
723 / 3 = 241
32 / 2 = 16
1972327 / 7 = 281761
...
MATHEMATICA
s={1, 2, 3, 11, 5, 6, 4}; t=Flatten[IntegerDigits[s]]; r=Select[Complement[Select[Range[60000], MemberQ[IntegerDigits[#], 0]==False&], s], Intersection[Partition[IntegerDigits[#], 2, 1], IntegerDigits[{14, 18, 34, 38, 54, 58, 74, 78, 94, 98}]]=={}&]; Do[c=1; While[d=IntegerDigits[r[[c]]]; Union[Table[IntegerQ[FromDigits[Take[Join[t, Take[d, i]], -d[[i]]]]/d[[i]]], {i, Length[d]}]]!={True}, c++]; AppendTo[s, r[[c]]]; r=Delete[r, c]; t=Take[Join[t, d], -9], {10002}]; s
(* Hans Havermann, Jul 12 2014 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Jul 06 2014
EXTENSIONS
More terms from Jean-Marc Falcoz, Jul 05 2014
STATUS
approved