A244496 Lexicographically earliest sequence S of integers with property that if a vertical line is drawn between any pair of adjacent digits p and q, say, the number Z formed by the p digits to the left of the line is divisible by p.

1, 2, 3, 11, 5, 6, 4, 8, 12, 13, 15, 21, 22, 24, 17, 16, 25, 19, 7, 23, 27, 9, 28, 41, 51, 31, 26, 42, 32, 43, 52, 44, 45, 35, 55, 59, 111, 53, 29, 56, 48, 46, 112, 57, 36, 33, 115, 71, 61, 121, 116, 81, 122, 123, 124, 39, 125, 91, 62, 119, 117, 126, 128, 82, 64, 47, 151, 37, 129, 152, 84, 83, 153

Offset: 1

Author

N. J. A. Sloane, Jul 06 2014

Keywords

• nonn
• base

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

Examples

			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
...
		

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

Crossrefs

Cf. A243357, A244471.

Programs

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 *)

Extensions

More terms from Jean-Marc Falcoz, Jul 05 2014