A193408 Hill numbers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 121, 131, 141, 151, 161, 171, 181, 191, 222, 232, 242, 252, 262, 272, 282, 292, 333, 343, 353, 363, 373, 383, 393, 444, 454, 464, 474, 484, 494, 555, 565, 575, 585, 595, 666, 676, 686, 696

Offset

1,2

Comments

Another version of mountain numbers (A134941) and A193407.

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.

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

Superset of A110784. - R. J. Mathar, Aug 07 2011

Links

Table of n, a(n) for n=1..57.

Example

Illustration using a term of this sequence, 4566664:
  .  .  6  6  6  6  .
  .  5  .  .  .  .  .
  4  .  .  .  .  .  4

Mathematica

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 *)

Crossrefs

Cf. A110784, A134810, A134941, A193407.

Sequence in context: A295010 A257054 A110784 * A368944 A346217 A353729

Adjacent sequences: A193405 A193406 A193407 * A193409 A193410 A193411

Keyword

nonn,base

Author

Jaroslav Krizek, Jul 25 2011

Status

approved