An '''esthetic number''' is a positive integer where every adjacent digit differs from its neighbour by 1.


;E.G.

:* '''12''' is an esthetic number. One and two differ by 1.

:* '''5654''' is an esthetic number. Each digit is exactly 1 away from its neighbour.

:* '''890''' is '''not''' an esthetic number. Nine and zero differ by 9.


These examples are nominally in base 10 but the concept extends easily to numbers in other bases. Traditionally, single digit numbers ''are'' included in esthetic numbers; zero may or may not be. For our purposes, for this task, do not include zero (0) as an esthetic number. Do not include numbers with leading zeros.

Esthetic numbers are also sometimes referred to as stepping numbers.


;Task

:* Write a routine (function, procedure, whatever) to find esthetic numbers in a given base.

:* Use that routine to find esthetic numbers in bases '''2''' through '''16''' and display, here on this page, the esthectic numbers from index '''(base × 4)''' through index '''(base × 6)''', inclusive. (E.G. for base 2: 8th through 12th, for base 6: 24th through 36th, etc.)

:* Find and display, here on this page, the '''base 10''' esthetic numbers with a magnitude between '''1000''' and '''9999'''.

:* Stretch: Find and display, here on this page, the '''base 10''' esthetic numbers with a magnitude between '''1.0e8''' and '''1.3e8'''.


;Related task:
* &nbsp; [[Numbers_With_Equal_Rises_and_Falls|numbers with equal rises and falls]]


;See also:
:;*[[oeis:A033075|OEIS A033075 - Positive numbers n such that all pairs of consecutive decimal digits differ by 1]]
:;*[http://www.numbersaplenty.com/set/esthetic_number/ Numbers Aplenty - Esthetic numbers]
:;*[https://www.geeksforgeeks.org/stepping-numbers/ Geeks for Geeks - Stepping numbers]
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