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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.

%I A244496 #24 Jul 14 2014 21:20:07
%S A244496 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,
%T A244496 26,42,32,43,52,44,45,35,55,59,111,53,29,56,48,46,112,57,36,33,115,71,
%U A244496 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
%N 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.
%C A244496 "Lexicographically earliest" means in the sense of a sequence of integers, not digits.
%C A244496 S is infinite, of course, as it can always be extended with an integer (not yet present) containing only 1's.
%C A244496 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
%D A244496 Eric Angelini, Posting to Sequence Fans Mailing List, Jun 26 2014
%H A244496 Jean-Marc Falcoz, <a href="/A244496/b244496.txt">Table of n, a(n) for n = 1..10009</a>
%e A244496 Example:a) draw a line between 6 and 4, for instance -- thus p = 6:
%e A244496    S = 1,2,3,11,5,6|,4,
%e A244496 b) concatenate the last 6 digits before the line (to get Z):
%e A244496    Z = 231156
%e A244496 c) Z/p is an integer (indeed, Z/6 = 38526)
%e A244496 Here are notes on the initial terms:
%e A244496          Z / p = integer   (Z ends in p and has digit-length p)
%e A244496          1 / 1 = 1
%e A244496         12 / 2 = 6
%e A244496        123 / 3 = 41
%e A244496          1 / 1 = 1
%e A244496          1 / 1 = 1
%e A244496      23115 / 5 = 4623
%e A244496     231156 / 6 = 38526
%e A244496       1564 / 4 = 391
%e A244496   23115648 / 8 = 2889456
%e A244496          1 / 1 = 1
%e A244496         12 / 2 = 6
%e A244496          1 / 1 = 1
%e A244496        213 / 3 = 71
%e A244496          1 / 1 = 1
%e A244496      21315 / 5 = 4263
%e A244496         52 / 2 = 26
%e A244496          1 / 1 = 1
%e A244496         12 / 2 = 6
%e A244496         22 / 2 = 11
%e A244496         22 / 2 = 11
%e A244496       2224 / 4 = 556
%e A244496          1 / 1 = 1
%e A244496    1222417 / 7 = 174631
%e A244496          1 / 1 = 1
%e A244496     241716 / 6 = 40286
%e A244496         62 / 2 = 31
%e A244496      71625 / 5 = 14325
%e A244496          1 / 1 = 1
%e A244496 417162519 / 9 = 46351391
%e A244496    1625197 / 7 = 232171
%e A244496         72 / 2 = 36
%e A244496        723 / 3 = 241
%e A244496         32 / 2 = 16
%e A244496    1972327 / 7 = 281761
%e A244496 ...
%t A244496 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
%t A244496 (* _Hans Havermann_, Jul 12 2014 *)
%Y A244496 Cf. A243357, A244471.
%K A244496 nonn,base
%O A244496 1,2
%A A244496 _N. J. A. Sloane_, Jul 06 2014
%E A244496 More terms from _Jean-Marc Falcoz_, Jul 05 2014