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A296447
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Smallest integer N such that all numbers from 1 to n (n being N's rank in the sequence) can be built by the sum of contiguous digits of N.
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1
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1, 11, 12, 112, 113, 132, 1114, 1133, 1143, 11134, 11144, 11154, 11443, 111155, 111165, 111544, 111554, 256318, 1111555, 1111655, 1111665, 1115554, 1194332, 11111766, 11111776, 11116565, 11116665, 12337741, 12377441, 111116766, 111117676, 111117776, 111166665, 113777242, 123377741, 123777441
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OFFSET
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1,2
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COMMENTS
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The 18th term (256318) is peculiar: it is the only one among the first 43 terms of the sequence that doesn't start with 1 and it is the only one having a digit-sum (25) larger than its rank in the sequence (18).
Barry Schwarz has computed a(44) to a(59), the latter being the second term of the sequence not to start with 1; a(59) = 213388888552. Barry estimates that a(60) probably has at least 13 digits.
a(60) = 1111111999998 has indeed 13 digits. a(100) <= 11123999999999461. - Giovanni Resta, Aug 01 2019
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LINKS
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EXAMPLE
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The 18th term of the sequence is 256318. The 18 numbers from 1 to 18 can be built summing a certain set of contiguous digits of 256318: 1 is the digit 1; 2 is the digit 2; 3 is the digit 3; 4 is 3+1 (contiguous); 5 is the digit 5; 6 is the digit 6; 7 is 2+5 (contiguous); 8 is the digit 8; 9 is 6+3 (contiguous); 10 is 6+3+1 (contiguous); 11 is 5+6 (contiguous); 12 is 3+1+8 (contiguous); 13 is 2+5+6 (contiguous); 14 is 5+6+3 (contiguous); 15 is 5+6+3+1 (contiguous); 16 is 2+5+6+3 (contiguous); 17 is 2+5+6+3+1 (contiguous); 18 is 6+3+1+8 (contiguous).
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MATHEMATICA
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Array[With[{r = Range@ #}, SelectFirst[Range[10^6], SequenceCount[Union@ Map[Total, #] &@ Apply[Join, Table[Partition[#, i, 1], {i, Length@#}]] &@ IntegerDigits@ #, r] == 1 &]] &, 18] (* or *)
With[{s = Array[LengthWhile[#, # == 1 &] &@ Differences@ Union@ Map[Total, #] &@ Apply[Join, Table[Partition[#, i, 1], {i, Length@ #}]] &@ IntegerDigits@ # &, 10^6]}, SelectFirst[#, FreeQ[IntegerDigits@#, 0] &] & /@ Values@ PositionIndex@ s] (* Michael De Vlieger, Dec 13 2017 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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