A215009 Numbers which are "easy" to key on a computer numpad.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 20, 21, 23, 25, 32, 36, 41, 45, 47, 52, 54, 56, 58, 63, 65, 69, 74, 78, 85, 87, 89, 96, 98, 101, 120, 121, 123, 125, 141, 145, 147, 202, 210, 212, 214, 232, 236, 252, 254, 256, 258, 320, 321, 323, 325, 363, 365, 369, 410

Offset: 1

Author

Arkadiusz Wesolowski, Jul 31 2012

Keywords

• base
• dumb
• easy
• nonn

Comments

On a computer numpad, a number is "easy" to key in if each adjacent pair of digits in the number are adjacent - either horizontally or vertically.

Here are two ways to type these numbers. Example for 25:

1. Press the numpad "2" key. Then let go and press "5".

2. Press the "2" and slide your finger on the numeric keypad up to the "5".

Method 2 shows that the sequence contains only numbers in which every pair of adjacent digits are distinct.

Pressing a numeric key followed by "0" and pressing a numeric key is equivalent to selecting "101" or "202".

Examples

			25 is a term because the 2 and 5 keys are adjacent.
		

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000
• Wikipedia, Numeric keypad
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A082390. Subsequence of A043096.

Programs

Mathematica

lst = {}; Do[If[StringCount[ToString[n], {"00", "03", "04", "05", "06", "07", "08", "09", "11", "13", "15", "16", "17", "18", "19", "22", "24", "26", "27", "28", "29", "30", "31", "33", "34", "35", "37", "38", "39", "40", "42", "43", "44", "46", "48", "49", "50", "51", "53", "55", "57", "59", "60", "61", "62", "64", "66", "67", "68", "70", "71", "72", "73", "75", "76", "77", "79", "80", "81", "82", "83", "84", "86", "88", "90", "91", "92", "93", "94", "95", "97", "99", "102", "201"}] == 0, AppendTo[lst, n]], {n, 0, 410}]; lst

Python

from itertools import count, islice
m = {'0':'12', '1':'024', '2':'0135', '3':'26', '4':'157', '5':'2468', '6':'359', '7':'48', '8':'579', '9':'68'}
def c(r): return (r=='0' or r[0]!='0') and not ("102" in r or "201" in r)
def agen():
    reach = list("0123456789")
    for d in count(1):
        yield from (int(r) for r in reach if c(r))
        reach = [r + s for r in reach for s in m[r[-1]]]
print(list(islice(agen(), 62))) # Michael S. Branicky, Jul 05 2022