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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. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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, 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

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Last modified May 20 23:05 EDT 2022. Contains 353886 sequences. (Running on oeis4.)