Hello Math-Fun & SeqFans, Dan Hoey found this (finite) sequence -- do you think it is worth adding it to the OEIS ? I would say yes ! S = 4, 5, 6, 7, 8, 41, 51, 63, 72, 83, 200 (there are 4 digits between the two 4's 5 digits between the two 5's 6 digits between the two 6's 7 digits between the two 7's 8 digits between the two 8's 1 digit between the two 1's ... 0 digit between the two 0's) Best, É. --- [Dan Hoey]:

The best is 456784151637283200, which can be chunked into 4+5+6+7+8+41+51+63+72+83+200 = 540.

(...) There are 10216 such 18-digit strings, or 9060 such integers if we prohibit leading zeroes.

--- [Eric A., a week ago]: We are looking for an 18-digit integer (like 946131483695200285) where we have "d" digits between two d's (here: one digit between two 1's, zero digit between the two 0's, nine digits between the two 9's, etc.) Those 18 digits form thus 9 pairs of digits -- the 9 pairs being different one from another. Now cut this integer into chunks so to make a finite monotonically increasing sequence (like this one, for instance, among others): 9,46,131,483,695,200285 ... and we sum the terms: 9+46+131+483+695+200285 = 201649 Question: Find the integer which, properly chunked, will give the smallest possible sum. (...)