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A178000
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Largest n-digit prime with the maximum number of digits equal to 2.
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2
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2, 29, 229, 2221, 22229, 922223, 9222229, 22222223, 222222227, 7222222229, 22222222223, 522222222229, 9222222222229, 22222222222229, 222222222222227, 9222222222222227, 72222222222222221, 222222222222222221
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OFFSET
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1,1
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COMMENTS
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Select first for most 2's, then take the largest.
In more detail: To get a(n), look at the list of all the n-digit primes. Suppose k is the maximum number of 2's of any number on the list. Throw out any prime on the list that does not contain k 2's. Then a(n) = maximal number that is left on the list. - N. J. A. Sloane, Mar 20 2018
For n <= 1000, a(n) has at most two non-2's. What is the first n for which it has more than two? - Robert Israel, Mar 20 2018
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LINKS
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MAPLE
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# This program will return FAIL if a(n) has more than two digits <> 2.
f:= proc(n)
local k1, d2, k2, t;
for k1 in [9, 7, 3, 1] do if isprime(2/9*(10^n-1)+k1-2) then return 2/9*(10^n-1)+k1-2 fi od;
for d2 from n to 2 by -1 do
for k2 in [9, 8, 7, 6, 5, 4, 3] do
for k1 in [9, 7, 3, 1] do
t:= 2/9*(10^(n)-1)+(k2-2)*10^(d2-1) + k1-2;
if isprime(t) then return t fi;
od od od:
FAIL
end proc:
f(1):= 2:
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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