A385280 a(n) is the number of n-digit primes of which all digits except one are the same.

4, 20, 46, 43, 40, 53, 35, 49, 40, 38, 44, 52, 35, 45, 49, 42, 38, 57, 27, 45, 38, 47, 37, 52, 33, 45, 56, 38, 36, 65, 29, 56, 48, 40, 38, 58, 37, 33, 57, 40, 37, 61, 41, 39, 37, 44, 36, 55, 47, 43, 47, 43, 35, 62, 43, 46, 29, 35, 37, 56, 39, 41, 46, 48, 39, 74, 45, 34, 34, 35, 34, 67, 39, 45, 43

Offset: 1

Author

Robert Israel, Jun 24 2025

Keywords

• nonn
• base

Comments

a(n) is the number of n-digit primes obtained by changing one digit of an n-digit repdigit.

Examples

			a(5) = 40 because there are 40 5-digit primes of which all digits but one are the same, namely 10111, 11113, 11117, 11119, 11131, 11161, 11171, 11311, 11411, 16111, 22229, 23333, 31333, 33331, 33343, 33353, 33533, 38333, 44449, 47777, 49999, 59999, 67777, 71777, 76777, 77377, 77477, 77747, 77773, 77797, 77977, 79777, 79999, 88883, 94999, 97777, 98999, 99929, 99989, 99991.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A004022, A010785, A084673, A241206.

Essentially the same as A258915.

Programs

Maple

f:= proc(n)
     local i,j,m, m2, t;
     t:= 0;
     for i from 1 to 9 do
       for j in {$0..9} minus {i} do
          if (n-1)*i + j mod 3 = 0 then next fi;
          if j = 0 then m2:= n-2 else m2:= n-1 fi;
          if not member(i,{1,3,7,9}) then m2:= 0 fi;
          t:= t + nops(select( isprime,{seq((10^n-1)/9*i + 10^m*(j-i),m=0..m2)}))
     od od;
     t
end proc:
f(1):= 4: f(2):= 20:
map(f, [$1..100]);

Python

from gmpy2 import is_prime, digits
def a(n):
    Rn = (10**n-1)//9
    return len(set(t for d in range(1, 10) for i in range(n if d in {1, 3, 7, 9} else 1) for c in set(range(-d, 10-d))-{0} if len(digits(t:=d*Rn+c*10**i))==n and is_prime(t)))
print([a(n) for n in range(1, 76)]) # Michael S. Branicky, Jun 25 2025