bonanova Posted March 29, 2009 Report Share Posted March 29, 2009 Consider the integer sequence {a1, a2, a3, ..., ai, ....} where ai = i + Floor {.5 + i.5} And Floor {x} = greatest integer not greater than x What is special about this sequence?. Quote Link to comment Share on other sites More sharing options...
0 Izzy Posted March 29, 2009 Report Share Posted March 29, 2009 What does 'Floor {.5 + i5}' mean? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 29, 2009 Author Report Share Posted March 29, 2009 What does 'Floor {.5 + i5}' mean? It means greatest integer [whole number] that is not greater than {1/2 + square root[i]} Suppose i=2: 1/2 + sqrt[2] = .5 + 1.4142 = 1.9142. Floor {1.9142} = 1. In other words, round down to the next lowest integer. Quote Link to comment Share on other sites More sharing options...
0 Izzy Posted March 29, 2009 Report Share Posted March 29, 2009 I don't know how to put this in mathy terms, but if you plug in numbers, you get two 1's, four 2's, six 3's, eight 4's, and I assume it goes on forever. Because, plug in 20, you get 4, which is the eight term. Meaning the next ten terms should result as 5. 30 = 5. 42 = 6. 56 = 7. 72 = 8. 90 = 9. 110 = 10. And I really cba to do it any further, and I'm really not capable of coming up with a proof, but yeah. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 29, 2009 Report Share Posted March 29, 2009 Consider the integer sequence {a1, a2, a3, ..., ai, ....} where ai = i + Floor {.5 + i.5} And Floor {x} = greatest integer not greater than x What is special about this sequence?. It is the sequence of all counting numbers except the perfect squares. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 29, 2009 Report Share Posted March 29, 2009 The series counts up in 1's but skips 1 after 2 terms then 4 terms then 6...... so it wil jump 1 every 2^x terms Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 29, 2009 Report Share Posted March 29, 2009 Consider the integer sequence {a1, a2, a3, ..., ai, ....} where ai = i + Floor {.5 + i.5} And Floor {x} = greatest integer not greater than x What is special about this sequence?.Its the counting numbers, but it skips all of the squares (1²=1, 2²=4, 3²=6, 4²=16, etc). Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 30, 2009 Report Share Posted March 30, 2009 (edited) Its the counting numbers, but it skips all of the squares (1²=1, 2²=4, 3²=6, 4²=16, etc). crapp... I forgot to add in the .5 *bangs head on wall* in the absence of the .5 in the "trunc" (floor) operation, the below is correct. however, with the .5 thrown in there, it is the answer quoted above me. Therefore, anytime that i is a perfect square, the count will increase by two. Anytime that i is NOT a perfect square, the count increases by one. see the attachment for the excel version of the "equation" Book 2 is the proper one for the puzzle. Book 1 is what I erroneously created and left off the .5Book1.xlsBook2.xls Edited March 30, 2009 by spikejones Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted April 1, 2009 Author Report Share Posted April 1, 2009 It is the sequence of all counting numbers except the perfect squares. Yes. Exactly. Elessar Adan has it also. I thought it was interesting.... Quote Link to comment Share on other sites More sharing options...
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bonanova
Consider the integer sequence {a1, a2, a3, ..., ai, ....} where ai = i + Floor {.5 + i.5}
And Floor {x} = greatest integer not greater than x
What is special about this sequence?.
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