A280594 Nonnegative numbers whose digits can be formed by typing adjacent keys on a 123-456-789-X0X keypad without repeating a digit.

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, 69, 74, 78, 80, 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, 580, 587, 589, 632, 652, 654, 658, 698, 741

Offset: 1

Author

FUNG Cheok Yin, Jan 06 2017

Keywords

• nonn
• fini
• base
• full

Comments

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

A subsequence of A010784. - FUNG Cheok Yin, Jul 05 2018

Examples

			The keypad is:
+---+---+---+
| 1 | 2 | 3 |
+---+---+---+
| 4 | 5 | 6 |
+---+---+---+
| 7 | 8 | 9 |
+---+---+---+
| x | 0 | x |
+---+---+---+
It is visibly obvious that 2580 can be formed on the keypad.
		

Links

• FUNG Cheok Yin, Table of n, a(n) for n = 1..723

Crossrefs

Cf. A010784, A280593, A280595.

Programs

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 <-> 0, 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], Range[0, 9]], 1];
A280594 = Sort[Join[r, FromDigits /@ Flatten[ff, 1]]] (* Jean-François Alcover, Jan 07 2017 *)

Extensions

Initial 0 prefixed by N. J. A. Sloane, Feb 05 2017