login
A280593
Natural numbers whose digits can be formed by typing adjacent keys on a 123-456-789 keypad without repeating a digit.
7
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, 74, 78, 85, 87, 89, 96, 98, 123, 125, 145, 147, 214, 236, 254, 256, 258, 321, 325, 365, 369, 412, 452, 456, 458, 478, 521, 523, 541, 547, 563, 569, 587, 589, 632, 652, 654, 658, 698, 741, 745, 785, 789
OFFSET
1,2
COMMENTS
A subsequence of A010784. - FUNG Cheok Yin, Jul 05 2018
LINKS
FUNG Cheok Yin, C++ program
EXAMPLE
The keypad is:
+---+---+---+
| 1 | 2 | 3 |
+---+---+---+
| 4 | 5 | 6 |
+---+---+---+
| 7 | 8 | 9 |
+---+---+---+
It is visibly obvious that 2589 can be formed on the keypad.
MATHEMATICA
g = Graph[{1 <-> 2, 1 <-> 4,
2 <-> 1, 2 <-> 3, 2 <-> 5,
3 <-> 2, 3 <-> 6,
4 <-> 1, 4 <-> 5, 4 <-> 7,
5 <-> 2, 5 <-> 4, 5 <-> 6, 5 <-> 8,
6 <-> 3, 6 <-> 5, 6 <-> 9,
7 <-> 4, 7 <-> 8,
8 <-> 5, 8 <-> 7, 8 <-> 9,
9 <-> 6, 9 <-> 8}];
f[{a_, b_}] := FindPath[g, a, b, Infinity, All]
ff = f /@ Flatten[Outer[List, r = Range[9], r], 1];
A280593 = Sort[Join[r, FromDigits /@ Flatten[ff, 1]]] (* Jean-François Alcover, Jan 06 2017 *)
CROSSREFS
KEYWORD
nonn,fini,full,base
AUTHOR
FUNG Cheok Yin, Jan 06 2017
STATUS
approved