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%I #23 Sep 01 2022 03:45:33
%S 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,
%T 63,65,69,74,78,85,87,89,96,98,101,120,121,123,125,141,145,147,202,
%U 210,212,214,232,236,252,254,256,258,320,321,323,325,363,365,369,410
%N Numbers which are "easy" to key on a computer numpad.
%C 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.
%C Here are two ways to type these numbers. Example for 25:
%C 1. Press the numpad "2" key. Then let go and press "5".
%C 2. Press the "2" and slide your finger on the numeric keypad up to the "5".
%C Method 2 shows that the sequence contains only numbers in which every pair of adjacent digits are distinct.
%C Pressing a numeric key followed by "0" and pressing a numeric key is equivalent to selecting "101" or "202".
%H Arkadiusz Wesolowski, <a href="/A215009/b215009.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Numeric_keypad">Numeric keypad</a>
%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%e 25 is a term because the 2 and 5 keys are adjacent.
%t 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
%o (Python)
%o from itertools import count, islice
%o m = {'0':'12', '1':'024', '2':'0135', '3':'26', '4':'157', '5':'2468', '6':'359', '7':'48', '8':'579', '9':'68'}
%o def c(r): return (r=='0' or r[0]!='0') and not ("102" in r or "201" in r)
%o def agen():
%o reach = list("0123456789")
%o for d in count(1):
%o yield from (int(r) for r in reach if c(r))
%o reach = [r + s for r in reach for s in m[r[-1]]]
%o print(list(islice(agen(), 62))) # _Michael S. Branicky_, Jul 05 2022
%Y Cf. A082390. Subsequence of A043096.
%K base,dumb,easy,nonn
%O 1,3
%A _Arkadiusz Wesolowski_, Jul 31 2012
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