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 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. 2
 1, 2, 3, 2, 5, 22, 2, 5, 22, 309, 2, 5, 22, 309, 10431 (list; table; graph; refs; listen; history; text; internal format)
 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 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

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Last modified September 26 12:36 EDT 2021. Contains 347665 sequences. (Running on oeis4.)