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

1,3

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".

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Wikipedia, Numeric keypad

Index entries for 10-automatic sequences.

Example

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

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

Prog

(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

Crossrefs

Cf. A082390. Subsequence of A043096.

Sequence in context: A322605 A175740 A320321 * A281943 A120003 A353852

Adjacent sequences: A215006 A215007 A215008 * A215010 A215011 A215012

Keyword

base,dumb,easy,nonn

Author

Arkadiusz Wesolowski, Jul 31 2012

Status

approved