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

1,1

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

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

Crossrefs

Cf. A037057, A099656, A177999.

Sequence in context: A244599 A261268 A020460 * A036939 A342962 A342971

Adjacent sequences: A177997 A177998 A177999 * A178001 A178002 A178003

Keyword

nonn,base

Author

Lekraj Beedassy, May 17 2010

Status

approved