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, 777, 787, 797, 888, 898, 999, 1111, 1221, 1231, 1241, 1251, 1261, 1271, 1281, 1291, 1321, 1331

Offset: 1

Author

Jaroslav Krizek, Jul 25 2011

Keywords

• nonn
• base

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

Examples

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

Crossrefs

Cf. A110784, A134810, A134941, A193407.

Programs

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 *)