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A280593 Natural numbers whose digits can be formed by typing adjacent keys on a 123-456-789 keypad without repeating a digit.

%I A280593 #33 Jul 08 2018 02:36:38
%S A280593 1,2,3,4,5,6,7,8,9,12,14,21,23,25,32,36,41,45,47,52,54,56,58,63,65,69,
%T A280593 74,78,85,87,89,96,98,123,125,145,147,214,236,254,256,258,321,325,365,
%U A280593 369,412,452,456,458,478,521,523,541,547,563,569,587,589,632,652,654,658,698,741,745,785,789
%N A280593 Natural numbers whose digits can be formed by typing adjacent keys on a 123-456-789 keypad without repeating a digit.
%C A280593 A subsequence of A010784. - _FUNG Cheok Yin_, Jul 05 2018
%H A280593 FUNG Cheok Yin, <a href="/A280593/b280593.txt">Table of n, a(n) for n = 1..653</a>
%H A280593 FUNG Cheok Yin, <a href="/A280593/a280593.cpp.txt">C++ program</a>
%e A280593 The keypad is:
%e A280593 +---+---+---+
%e A280593 | 1 | 2 | 3 |
%e A280593 +---+---+---+
%e A280593 | 4 | 5 | 6 |
%e A280593 +---+---+---+
%e A280593 | 7 | 8 | 9 |
%e A280593 +---+---+---+
%e A280593 It is visibly obvious that 2589 can be formed on the keypad.
%t A280593 g = Graph[{1 <-> 2, 1 <-> 4,
%t A280593     2 <-> 1, 2 <-> 3, 2 <-> 5,
%t A280593     3 <-> 2, 3 <-> 6,
%t A280593     4 <-> 1, 4 <-> 5, 4 <-> 7,
%t A280593     5 <-> 2, 5 <-> 4, 5 <-> 6, 5 <-> 8,
%t A280593     6 <-> 3, 6 <-> 5, 6 <-> 9,
%t A280593     7 <-> 4, 7 <-> 8,
%t A280593     8 <-> 5, 8 <-> 7, 8 <-> 9,
%t A280593     9 <-> 6, 9 <-> 8}];
%t A280593 f[{a_, b_}] := FindPath[g, a, b, Infinity, All]
%t A280593 ff = f /@ Flatten[Outer[List, r = Range[9], r], 1];
%t A280593 A280593 = Sort[Join[r, FromDigits /@ Flatten[ff, 1]]] (* _Jean-François Alcover_, Jan 06 2017 *)
%Y A280593 Cf. A010784, A280594, A280595.
%K A280593 nonn,fini,full,base
%O A280593 1,2
%A A280593 _FUNG Cheok Yin_, Jan 06 2017