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A244496
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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.
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3
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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
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OFFSET
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1,2
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COMMENTS
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"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
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REFERENCES
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Eric Angelini, Posting to Sequence Fans Mailing List, Jun 26 2014
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LINKS
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Jean-Marc Falcoz, Table of n, a(n) for n = 1..10009
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EXAMPLE
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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
...
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A243357, A244471.
Sequence in context: A031335 A084743 A030391 * A039654 A075240 A229607
Adjacent sequences: A244493 A244494 A244495 * A244497 A244498 A244499
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KEYWORD
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nonn,base
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AUTHOR
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N. J. A. Sloane, Jul 06 2014
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EXTENSIONS
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More terms from Jean-Marc Falcoz, Jul 05 2014
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STATUS
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approved
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