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

%I A244192 #30 May 22 2025 10:21:39
%S A244192 0,0,0,97,71,91,77,61,47,47,19,27,37
%N A244192 a(n) = most common 2-digit ending for a prime < 10^n, or 0 if there is a tie.
%C A244192 a(3) = 0 because '83' and '57' both appear 6 times in the endings of primes < 1000.
%C A244192 a(4) = 0 because '19' and '23' both appear 35 times in the endings of primes < 10000.
%e A244192 For all primes < 100000 (10^5), the most common 2-digit ending is 97. Thus a(5) = 97.
%o A244192 (Python)
%o A244192 import sympy
%o A244192 from sympy import isprime
%o A244192 def prend(d,n):
%o A244192   lst = []
%o A244192   for k in range(10**n):
%o A244192     if isprime(k):
%o A244192       lst.append((k%10**d))
%o A244192   new = 0
%o A244192   newlst = []
%o A244192   for i in range(10**(d-1),10**d):
%o A244192     new = lst.count(i)
%o A244192     newlst.append(new)
%o A244192   newlst1 = newlst.copy()
%o A244192   a = max(newlst1)
%o A244192   newlst1[newlst1.index(a)] = 0
%o A244192   b = max(newlst1)
%o A244192   if a == b:
%o A244192     return 0
%o A244192   else:
%o A244192     return newlst.index(max(a,b)) + 10**(d-1)
%o A244192 n = 3
%o A244192 while n < 10:
%o A244192   print(prend(2,n),end=', ')
%o A244192   n += 1
%Y A244192 Cf. A244191, A244267.
%K A244192 nonn,base,hard,more
%O A244192 2,4
%A A244192 _Derek Orr_, Jun 22 2014
%E A244192 a(9)-a(12) from _Hiroaki Yamanouchi_, Jul 11 2014
%E A244192 a(13)-a(14) from _Giovanni Resta_, Oct 23 2018