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A215009
Numbers which are "easy" to key on a computer numpad.
4
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".
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
KEYWORD
base,dumb,easy,nonn
AUTHOR
STATUS
approved