A133568 Triangle: row n is least sequence of n positive integers such that A131655(n) distinct rational numbers are generated only from them using only +, -, * and / and each number in the row no more than once in a given expression.

1, 2, 3, 2, 5, 22, 2, 5, 22, 309, 2, 5, 22, 309, 10431

Offset

1,2

Comments

As in A131655, these operations are all considered to be the usual binary operations only; in particular, -x is not a permitted expression.

The list of rational numbers generated by row 5 does not contain a 1 or 0 and therefore it still might be possible to construct row 6 by using the numbers from row 5. Futhermore, one might conjecture that all subsequent rows fully contain the previous one. - Mikelis Emils Mikelsons, Sep 01 2021

Links

Table of n, a(n) for n=1..15.

Mikelis Emils Mikelsons, The list of rational numbers generated by row 5

Mikelis Emils Mikelsons, List of expressions for row 5

Example

Row 3: 2, 5, 22 generates these A131655(3)=89 distinct rational numbers:
-108, -100, -66, -39, -34, -25, -108/5, -20, -39/2, -19, -17, -15, -12,
-17/2, -22/3, -6, -54/11, -4, -3, -12/5, -39/22, -1/4, -3/22, -2/17, 1/55,
2/27, 1/11, 5/44, 2/17, 3/22, 5/24, 5/22, 1/4, 7/22, 2/5, 5/11,
39/22, 2, 11/5, 49/22, 12/5, 5/2, 3, 22/7, 4, 22/5, 24/5, 54/11, 5,
56/11, 6, 32/5, 7, 22/3, 17/2, 44/5, 10, 11, 12, 27/2, 15, 16, 17, 19,
39/2, 20, 108/5, 22, 112/5, 24, 49/2, 25, 27, 29, 32, 34, 39, 44, 49,
54, 55, 66, 100, 108, 110, 112, 120, 154, 220.
No smaller sequence of three positive integers generates this many distinct results.
Triangle begins:
  1;
  2, 3;
  2, 5, 22;
  2, 5, 22, 309;
  2, 5, 22, 309, 10431;
  ...

Crossrefs

Cf. A131655.

Sequence in context: A339645 A318956 A086507 * A120716 A084318 A084317

Adjacent sequences: A133565 A133566 A133567 * A133569 A133570 A133571

Keyword

nonn,tabl,hard,more

Author

Rick L. Shepherd, Sep 16 2007

Extensions

More terms by Mikelis Emils Mikelsons, Sep 01 2021

Status

approved