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%I #47 Jul 08 2018 02:36:22
%S 0,1,2,3,4,5,6,7,8,9,12,14,21,23,25,32,36,41,45,47,52,54,56,58,63,65,
%T 69,74,78,80,85,87,89,96,98,123,125,145,147,214,236,254,256,258,321,
%U 325,365,369,412,452,456,458,478,521,523,541,547,563,569,580,587,589,632,652,654,658,698,741
%N Nonnegative numbers whose digits can be formed by typing adjacent keys on a 123-456-789-X0X keypad without repeating a digit.
%C Number of terms < 10^k for k = 1,2,3,...: 10, 35, 82, 167, 281, 419, 547, 669, 723. - _Robert G. Wilson v_, Feb 06 2017
%C A subsequence of A010784. - _FUNG Cheok Yin_, Jul 05 2018
%H FUNG Cheok Yin, <a href="/A280594/b280594.txt">Table of n, a(n) for n = 1..723</a>
%e The keypad is:
%e +---+---+---+
%e | 1 | 2 | 3 |
%e +---+---+---+
%e | 4 | 5 | 6 |
%e +---+---+---+
%e | 7 | 8 | 9 |
%e +---+---+---+
%e | x | 0 | x |
%e +---+---+---+
%e It is visibly obvious that 2580 can be formed on the keypad.
%t g = Graph[{1 <-> 2, 1 <-> 4,
%t 2 <-> 1, 2 <-> 3, 2 <-> 5,
%t 3 <-> 2, 3 <-> 6,
%t 4 <-> 1, 4 <-> 5, 4 <-> 7,
%t 5 <-> 2, 5 <-> 4, 5 <-> 6, 5 <-> 8,
%t 6 <-> 3, 6 <-> 5, 6 <-> 9,
%t 7 <-> 4, 7 <-> 8,
%t 8 <-> 0, 8 <-> 5, 8 <-> 7, 8 <-> 9,
%t 9 <-> 6, 9 <-> 8}];
%t f[{a_, b_}] := FindPath[g, a, b, Infinity, All]
%t ff = f /@ Flatten[Outer[List, r = Range[9], Range[0, 9]], 1];
%t A280594 = Sort[Join[r, FromDigits /@ Flatten[ff, 1]]] (* _Jean-François Alcover_, Jan 07 2017 *)
%Y Cf. A010784, A280593, A280595.
%K nonn,fini,base,full
%O 1,3
%A _FUNG Cheok Yin_, Jan 06 2017
%E Initial 0 prefixed by _N. J. A. Sloane_, Feb 05 2017
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