A193408 - OEIS

%I #36 Aug 03 2022 02:34:43

%S 1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,111,121,131,141,151,161,

%T 171,181,191,222,232,242,252,262,272,282,292,333,343,353,363,373,383,

%U 393,444,454,464,474,484,494,555,565,575,585,595,666,676,686,696

%N Hill numbers.

%C Another version of mountain numbers (A134941) and A193407.

%C For n > 20 the structure of digits represents a hill. The first digit is equal to the last digit (1 - 9). The first digits are in nondecreasing order. The last digits are in nonincreasing order. The numbers may have more than one largest digit. Sequence is infinite.

%C Superset of mountain numbers (A134941), A193407, and Giza numbers (A134810).

%C Superset of A110784. - _R. J. Mathar_, Aug 07 2011

%e Illustration using a term of this sequence, 4566664:

%e   .  .  6  6  6  6  .

%e   .  5  .  .  .  .  .

%e   4  .  .  .  .  .  4

%t nonz[v_] := Select[v,#!=0 &]; hillQ[n_] := Module[{d=IntegerDigits[n]}, If[d[[1]] != d[[-1]], Return[False]]; MemberQ[{{},{0},{-2}}, nonz@ Differences@ Sign@ nonz@ Differences@d]]; Select[Range[1000], hillQ] (* _Amiram Eldar_, Dec 19 2018 *)

%Y Cf. A110784, A134810, A134941, A193407.

%K nonn,base

%O 1,2

%A _Jaroslav Krizek_, Jul 25 2011