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

1,2

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

Cf. A243357, A244471.

Sequence in context: A031335 A084743 A030391 * A039654 A075240 A347358

Adjacent sequences: A244493 A244494 A244495 * A244497 A244498 A244499

Keyword

nonn,base

Author

N. J. A. Sloane, Jul 06 2014

Extensions

More terms from Jean-Marc Falcoz, Jul 05 2014

Status

approved