cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

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

Original entry on oeis.org

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

Views

Author

FUNG Cheok Yin, Jan 06 2017

Keywords

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

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

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

Original entry on oeis.org

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, 70, 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, 470, 478, 521, 523, 541, 547, 563, 569, 580, 587, 589, 632, 652, 654, 658
Offset: 1

Views

Author

FUNG Cheok Yin, Jan 06 2017

Keywords

Comments

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

Examples

			The keypad is:
+---+---+---+
| 1 | 2 | 3 |
+---+---+---+
| 4 | 5 | 6 |
+---+---+---+
| 7 | 8 | 9 |
+---+---+---+
|   0   | x |
+---+---+---+
It is visibly obvious that 5807 can be formed on the keypad.

Links

Crossrefs

Cf. A010784, A280593, A280594.

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 <-> 0, 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];
A280595 = Sort[Join[r, FromDigits /@ Flatten[ff, 1]]] (* Jean-François Alcover, Jan 07 2017 *)

Extensions

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

A281942 Nonnegative numbers whose digits can be formed by typing adjacent keys on a 123-456-789-0XX keypad without repeating a digit.

Original entry on oeis.org

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, 70, 74, 78, 85, 87, 89, 96, 98, 123, 125, 145, 147, 214, 236, 254, 256, 258, 321, 325, 365, 369, 412, 452, 456, 458, 470, 478, 521, 523, 541, 547, 563, 569, 587, 589, 632, 652, 654, 658, 698, 741
Offset: 1

Views

Author

FUNG Cheok Yin, Feb 02 2017

Keywords

Comments

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

Examples

			The keypad is:
+---+---+---+
| 1 | 2 | 3 |
+---+---+---+
| 4 | 5 | 6 |
+---+---+---+
| 7 | 8 | 9 |
+---+---+---+
| 0 | x | x |
+---+---+---+
It is visibly obvious that 470 can be formed on the keypad.

Links

Crossrefs

Cf. A010784, A280593, A280594, A280595, A281943, A215009.

Extensions

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

A281943 Nonnegative numbers whose digits can be formed by typing adjacent keys on a 789-456-123-00X keypad without repeating a digit.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 20, 21, 23, 25, 32, 36, 41, 45, 47, 52, 54, 56, 58, 63, 65, 69, 74, 78, 85, 87, 89, 96, 98, 102, 120, 123, 125, 145, 147, 201, 210, 214, 236, 254, 256, 258, 320, 321, 325, 365, 369, 410, 412, 452, 456, 458, 478, 520, 521, 523, 541, 547, 563, 569, 587
Offset: 1

Views

Author

FUNG Cheok Yin, Feb 02 2017

Keywords

Comments

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

Examples

			The keypad is:
+---+---+---+
| 7 | 8 | 9 |
+---+---+---+
| 4 | 5 | 6 |
+---+---+---+
| 1 | 2 | 3 |
+---+---+---+
|   0   | x |
+---+---+---+
It is visibly obvious that 5210 can be formed on the keypad.

Links

Crossrefs

Cf. A010784, A280593, A280594, A280595, A281942, A215009.

Extensions

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

A283161 Natural numbers whose digits can be formed by typing non-adjacent keys on a 123-456-789 keypad without repeating a digit.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 15, 16, 17, 18, 19, 24, 26, 27, 28, 29, 31, 34, 35, 37, 38, 39, 42, 43, 46, 48, 49, 51, 53, 57, 59, 61, 62, 64, 67, 68, 71, 72, 73, 75, 76, 79, 81, 82, 83, 84, 86, 91, 92, 93, 94, 95, 97, 135, 137, 138, 139, 153, 157, 159, 167, 168, 173, 175, 176, 179, 183, 186, 193, 195
Offset: 1

Views

Author

FUNG Cheok Yin, Mar 02 2017

Keywords

Comments

Or say numbers which are "very difficult" to be typed on a keypad without the zero. (See description of A215009.)

Examples

			The keypad is:
+-----+
|1|2|3|
+-+-+-+
|4|5|6|
+-+-+-+
|7|8|9|
+-+-+-+
It is visibly obvious that 168 can be formed on the keypad, and each pairwise digits of 168 are not adjacent.

Links

Crossrefs

Cf. A280593, A215009, A006506(3)

Programs

  • Mathematica
    no = IntegerDigits @ {12,14,23,25,34,36,45,47,56,58,69,78,89}; Sort[ FromDigits /@ Flatten[ Permutations /@ Select[ Subsets[ Range@ 9, {1, 9}], Intersection[ Subsets[#, {2}], no] == {} &], 1]] (* Giovanni Resta, Apr 06 2017 *)

A322511 Nonnegative numbers whose digits can be formed by typing adjacent keys on a 123-456-789 keypad without repeating a digit and without changing direction.

Original entry on oeis.org

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, 147, 258, 321, 369, 456, 654, 741, 789, 852, 963, 987
Offset: 1

Views

Author

Jason Jewell, Dec 13 2018

Keywords

Comments

Subsequence of A280593.
Diagonal moves are not allowed.

Examples

			The keypad is:
+---+---+---+
| 1 | 2 | 3 |
+---+---+---+
| 4 | 5 | 6 |
+---+---+---+
| 7 | 8 | 9 |
+---+---+---+
258 can be formed in a straight line, while 256 cannot, even though 256 is formed with adjacent digits. Therefore 258 is a part of this sequence while 256 is not.

Crossrefs

Cf. A280593, A280594, A280595, A281942.
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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