A032865 Numbers whose base-10 representation Sum_{i=0..m} d(i)*10^i has d(m) > d(m-1) < d(m-2) > ...

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98, 101, 102, 103, 104, 105, 106, 107

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

Every other digit must be strictly less than its neighbor(s). - M. F. Hasler, Oct 05 2018

Links

• M. F. Hasler, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A032858 .. A032864 for base-3 .. 9 variants.

Programs

Mathematica

sdQ[n_]:=Module[{s=Sign[Differences[IntegerDigits[n, 10]]]}, 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),(n[i-1]-n[i])*(-1)^i>0||return) \\ M. F. Hasler, Oct 05 2018

Extensions

Name corrected and cross-references and a(1) = 0 prepended by M. F. Hasler, Oct 05 2018