A244189 a(n) = most common final digit for a prime with n digits, or 0 if there is a tie.

0, 3, 7, 3, 7, 3, 7, 7, 3, 3, 1, 7, 3, 7

Offset

1,2

Links

Table of n, a(n) for n=1..14.

Example

Primes with two digits are {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}. The most frequent last digit is a 3. Thus a(2) = 3.

Mathematica

Join[{0}, Table[SortBy[Tally[Mod[Prime[Range[1+PrimePi[10^d], PrimePi[10^(d+1)]]], 10]], Last][[-1, 1]], {d, 8}]] (* The program generates the first 9 terms of the sequence. *) (* Harvey P. Dale, Sep 30 2025 *)

Prog

(Python)
import sympy
from sympy import isprime
def end(d, n):
  lst = []
  for k in range(10**(d-1), 10**d):
    num = ''
    count = 0
    for i in range(10**(n-d-1), 10**(n-d)):
      if isprime(int(str(i)+str(k))):
        count += 1
    lst.append(count)
  a = max(lst)
  lst[lst.index(a)] = 0
  b = max(lst)
  if a == b:
    return 0
  else:
    return max(a, b) + 10**(d-1)
n = 2
while n < 10:
  print(end(1, n), end=', ')
  n += 1

Crossrefs

Cf. A244190.

Sequence in context: A244191 A161973 A010705 * A375152 A200481 A016665

Adjacent sequences: A244186 A244187 A244188 * A244190 A244191 A244192

Keyword

nonn,base,hard,more

Author

Derek Orr, Jun 22 2014

Extensions

a(9)-a(14) from Hiroaki Yamanouchi, Jul 10 2014

Status

approved