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

1,1

Comments

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

Links

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

Example

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.

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]);

Prog

(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

Crossrefs

Cf. A004022, A010785, A084673, A241206.

Essentially the same as A258915.

Sequence in context: A163365 A145194 A164924 * A033579 A294630 A160799

Adjacent sequences: A385277 A385278 A385279 * A385281 A385282 A385283

Keyword

nonn,base

Author

Robert Israel, Jun 24 2025

Status

approved