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Numbers whose base-8 representation Sum_{i=0..m} d(i)*8^i has d(m) > d(m-1) < d(m-2) > ...
3

%I #20 Oct 10 2018 09:07:15

%S 0,1,2,3,4,5,6,7,8,16,17,24,25,26,32,33,34,35,40,41,42,43,44,48,49,50,

%T 51,52,53,56,57,58,59,60,61,62,65,66,67,68,69,70,71,129,130,131,132,

%U 133,134,135,138,139,140,141,142,143,193,194,195

%N Numbers whose base-8 representation Sum_{i=0..m} d(i)*8^i has d(m) > d(m-1) < d(m-2) > ...

%C Base-8 digits must be strictly alternating in size: every other digit must be strictly less than its neighbor(s). Also: numbers whose base-8 expansion, considered as a decimal number, is in A032865 = the base-10 variant of this sequence. - _M. F. Hasler_, Oct 05 2018

%e From _M. F. Hasler_, Oct 05 2018: (Start)

%e The base-8 representation of 7, 8, 16, 17, 24, 25, 26, 32, 33 is 7, 10, 20, 21, 30, 31, 32, 40, 41.

%e Numbers 61, 62, 65, 66, ..., 70, 71, 129, 130, ... have the base-8 expansion 76, 77, 101, 102, ..., 106, 107, 201, 202, ... (End)

%t sdQ[n_]:=Module[{s=Sign[Differences[IntegerDigits[n, 8]]]}, s==PadRight[{}, Length[s], {-1, 1}]]; Select[Range[0, 700], sdQ] (* _Vincenzo Librandi_, Oct 06 2018 *)

%o (PARI) is(n)=!for(i=2,#n=digits(n,8),(n[i-1]-n[i])*(-1)^i>0||return) \\ _M. F. Hasler_, Oct 05 2018

%Y Cf. A032858, A032859, A032860, A032861, A032862, this sequence, A032864, A032865 for bases 3 to 10.

%K nonn,base

%O 1,3

%A _Clark Kimberling_

%E a(1) = 0 added by _Vincenzo Librandi_, Oct 06 2018