OFFSET
1,2
COMMENTS
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
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..85 (terms 1..59 from Jean-Marc Falcoz and Barry Schwarz)
EXAMPLE
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).
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Dec 13 2017
STATUS
approved