A244471 -id:A244471 - cp's OEIS frontend

A243357 Lexicographically earliest sequence of integers with property that if a vertical line is drawn between any pair of adjacent digits, the number Z formed by the digits to the left of the line is divisible by the final digit of Z.

1, 2, 3, 5, 11, 12, 4, 8, 7, 13, 6, 9, 15, 17, 16, 21, 22, 23, 24, 25, 26, 31, 28, 27, 51, 52, 32, 41, 53, 33, 35, 55, 36, 39, 61, 29, 62, 19, 63, 57, 64, 42, 44, 37, 56, 45, 65, 111, 112, 48, 66, 91, 113, 68, 43, 92, 46, 69, 93, 115, 116, 81, 95, 121, 96, 82, 119, 99, 122, 49, 71, 124, 84, 47, 72, 85, 67, 75, 59, 123, 117, 77, 73, 125

Offset: 1

N. J. A. Sloane, Jun 25 2014

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, 114, 118, 134, 138, 141, 142, 143, 144, 145, 146, 147, 148, 149, 154, 158, 174, ... (see A244033, A244034). - Giovanni Resta, Jun 25 2014; Jun 26 2014

			1 / 1 = 1
12 / 2 = 6
123 / 3 = 41
1235 / 5 = 247
12351 / 1 = 12351
123511 / 1 = 123511
1235111 / 1 = 1235111
12351112 / 2 = 6175556
123511124 / 4 = 30877781
1235111248 / 8 = 154388906 ...

Eric Angelini, Posting to Sequence Fans Mailing List, Jun 24 2014

Giovanni Resta, Table of n, a(n) for n = 1..10000
Giovanni Resta, First 10^6 terms (2.2 MB zip file)

Cf. A244033, A244034.

A244471 and A244496 are sister sequences.

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.

Original entry on oeis.org

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

N. J. A. Sloane, Jul 06 2014

"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

			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
...

Eric Angelini, Posting to Sequence Fans Mailing List, Jun 26 2014

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10009

Cf. A243357, A244471.

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 *)

More terms from Jean-Marc Falcoz, Jul 05 2014

cp's OEIS Frontend

A243357 Lexicographically earliest sequence of integers with property that if a vertical line is drawn between any pair of adjacent digits, the number Z formed by the digits to the left of the line is divisible by the final digit of Z.

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