A032863 Numbers whose base-8 representation Sum_{i=0..m} d(i)*8^i has d(m) > d(m-1) < d(m-2) > ...

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, 51, 52, 53, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 129, 130, 131, 132, 133, 134, 135, 138, 139, 140, 141, 142, 143, 193, 194, 195

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

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

Examples

			From _M. F. Hasler_, Oct 05 2018: (Start)
The base-8 representation of 7, 8, 16, 17, 24, 25, 26, 32, 33 is 7, 10, 20, 21, 30, 31, 32, 40, 41.
Numbers 61, 62, 65, 66, ..., 70, 71, 129, 130, ... have the base-8 expansion 76, 77, 101, 102, ..., 106, 107, 201, 202, ... (End)
		

Crossrefs

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

Programs

Mathematica

 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 *)

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

Extensions

a(1) = 0 added by Vincenzo Librandi, Oct 06 2018