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2007 Harvard-MIT Mathematics Tournament
12
12
Part of
2007 Harvard-MIT Mathematics Tournament
Problems
(1)
2007 Guts #12: A Sequence of Primes
Source:
6/22/2012
Let
A
11
A_{11}
A
11
denote the answer to problem
11
11
11
. Determine the smallest prime
p
p
p
such that the arithmetic sequence
p
,
p
+
A
11
,
p
+
2
A
11
,
⋯
p,p+A_{11},p+2A_{11},\cdots
p
,
p
+
A
11
,
p
+
2
A
11
,
⋯
begins with the largest number of primes.There is just one triple of possible
(
A
10
,
A
11
,
A
12
)
(A_{10},A_{11},A_{12})
(
A
10
,
A
11
,
A
12
)
of answers to these three problems. Your team will receive credit only for answers matching these. (So, for example, submitting a wrong answer for problem
11
11
11
will not alter the correctness of your answer to problem
12
12
12
.)
arithmetic sequence