cp's OEIS Frontend

A280595 Nonnegative numbers whose digits can be formed by typing adjacent keys on a 123-456-789-00X keypad without repeating a digit.

%I A280595 #39 Jul 08 2018 02:36:43
%S A280595 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 A280595 69,70,74,78,80,85,87,89,96,98,123,125,145,147,214,236,254,256,258,
%U A280595 321,325,365,369,412,452,456,458,470,478,521,523,541,547,563,569,580,587,589,632,652,654,658
%N A280595 Nonnegative numbers whose digits can be formed by typing adjacent keys on a 123-456-789-00X keypad without repeating a digit.
%C A280595 A subsequence of A010784. - _FUNG Cheok Yin_, Jul 05 2018
%H A280595 FUNG Cheok Yin, <a href="/A280595/b280595.txt">Table of n, a(n) for n = 1..1082</a>
%e A280595 The keypad is:
%e A280595 +---+---+---+
%e A280595 | 1 | 2 | 3 |
%e A280595 +---+---+---+
%e A280595 | 4 | 5 | 6 |
%e A280595 +---+---+---+
%e A280595 | 7 | 8 | 9 |
%e A280595 +---+---+---+
%e A280595 |   0   | x |
%e A280595 +---+---+---+
%e A280595 It is visibly obvious that 5807 can be formed on the keypad.
%t A280595 g = Graph[{1 <-> 2, 1 <-> 4,
%t A280595     2 <-> 1, 2 <-> 3, 2 <-> 5,
%t A280595     3 <-> 2, 3 <-> 6,
%t A280595     4 <-> 1, 4 <-> 5, 4 <-> 7,
%t A280595     5 <-> 2, 5 <-> 4, 5 <-> 6, 5 <-> 8,
%t A280595     6 <-> 3, 6 <-> 5, 6 <-> 9,
%t A280595     7 <-> 0, 7 <-> 4, 7 <-> 8,
%t A280595     8 <-> 0, 8 <-> 5, 8 <-> 7, 8 <-> 9,
%t A280595     9 <-> 6, 9 <-> 8}];
%t A280595 f[{a_, b_}] := FindPath[g, a, b, Infinity, All]
%t A280595 ff = f /@ Flatten[Outer[List, r = Range[9], Range[0, 9]], 1];
%t A280595 A280595 = Sort[Join[r, FromDigits /@ Flatten[ff, 1]]] (* _Jean-François Alcover_, Jan 07 2017 *)
%Y A280595 Cf. A010784, A280593, A280594.
%K A280595 nonn,base,fini,full
%O A280595 1,3
%A A280595 _FUNG Cheok Yin_, Jan 06 2017
%E A280595 Initial 0 added by _N. J. A. Sloane_, Feb 05 2017