A244192 a(n) = most common 2-digit ending for a prime < 10^n, or 0 if there is a tie.

0, 0, 0, 97, 71, 91, 77, 61, 47, 47, 19, 27, 37

Offset: 2

Author

Derek Orr, Jun 22 2014

Keywords

• nonn
• base
• hard
• more

Comments

a(3) = 0 because '83' and '57' both appear 6 times in the endings of primes < 1000.

a(4) = 0 because '19' and '23' both appear 35 times in the endings of primes < 10000.

Examples

			For all primes < 100000 (10^5), the most common 2-digit ending is 97. Thus a(5) = 97.
		

Crossrefs

Cf. A244191, A244267.

Programs

Python

import sympy
from sympy import isprime
def prend(d,n):
  lst = []
  for k in range(10**n):
    if isprime(k):
      lst.append((k%10**d))
  new = 0
  newlst = []
  for i in range(10**(d-1),10**d):
    new = lst.count(i)
    newlst.append(new)
  newlst1 = newlst.copy()
  a = max(newlst1)
  newlst1[newlst1.index(a)] = 0
  b = max(newlst1)
  if a == b:
    return 0
  else:
    return newlst.index(max(a,b)) + 10**(d-1)
n = 3
while n < 10:
  print(prend(2,n),end=', ')
  n += 1

Extensions

a(9)-a(12) from Hiroaki Yamanouchi, Jul 11 2014

a(13)-a(14) from Giovanni Resta, Oct 23 2018