A032863 - OEIS

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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

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OFFSET

1,3

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

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

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)

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 *)

PROG

(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

CROSSREFS

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

Sequence in context: A319724 A097546 A004837 * A032887 A023790 A032943

Adjacent sequences: A032860 A032861 A032862 * A032864 A032865 A032866

KEYWORD

nonn,base

AUTHOR

Clark Kimberling

EXTENSIONS

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

STATUS

approved