A178000 Largest n-digit prime with the maximum number of digits equal to 2.

2, 29, 229, 2221, 22229, 922223, 9222229, 22222223, 222222227, 7222222229, 22222222223, 522222222229, 9222222222229, 22222222222229, 222222222222227, 9222222222222227, 72222222222222221, 222222222222222221

Offset: 1

Author

Lekraj Beedassy, May 17 2010

Keywords

• nonn
• base

Comments

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

Links

• Robert Israel, Table of n, a(n) for n = 1..999

Crossrefs

Cf. A037057, A099656, A177999.

Programs

Maple

# 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:
seq(f(n),n=1..30); # Robert Israel, Mar 20 2018