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Numbers whose base-6 representation Sum_{i=0..m} d(i)*6^i has d(m) > d(m-1) < d(m-2) > ...
2

%I #22 Aug 22 2021 09:21:01

%S 0,1,2,3,4,5,6,12,13,18,19,20,24,25,26,27,30,31,32,33,34,37,38,39,40,

%T 41,73,74,75,76,77,80,81,82,83,109,110,111,112,113,116,117,118,119,

%U 123,124,125,145,146,147,148,149,152,153,154,155

%N Numbers whose base-6 representation Sum_{i=0..m} d(i)*6^i has d(m) > d(m-1) < d(m-2) > ...

%t sdQ[n_]:=Module[{s=Sign[Differences[IntegerDigits[n,6]]]},s==PadRight[{}, Length[ s],{-1,1}]]; Select[Range[0,200],sdQ] (* _Harvey P. Dale_, Dec 15 2017 *)

%Y Cf. A007092.

%Y Cf. A032858..A032865 for bases 3..10.

%Y Cf. A306106..A306111 and A297147 for bases 3..9 and 10.

%K nonn,base

%O 1,3

%A _Clark Kimberling_

%E a(1)=0 inserted by _Georg Fischer_, Dec 18 2020