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A348176 Numbers m such that the number of symmetrically distributed consecutive primes centered at m sets a new record.

%I A348176 #14 Nov 21 2021 09:55:47
%S A348176 1,2,4,5,9,12,30,165,8021811,1071065190,1613902650,1797595815015,
%T A348176 633925574060895
%N A348176 Numbers m such that the number of symmetrically distributed consecutive primes centered at m sets a new record.
%C A348176 Conjecture: This sequence is infinite.
%e A348176 n    a(n) = m   A346399(m)  Symmetrical consecutive primes centered at m
%e A348176 --  ----------  ----------  --------------------------------------------
%e A348176 1            1       0                           { }
%e A348176 2            2       1                           {2}
%e A348176 3            4       2                          {3,5}
%e A348176 4            5       3                         {3,5,7}
%e A348176 5            9       4                        {5,7,11,13}
%e A348176 6           12       6                     {5,7,11,13,17,19}
%e A348176 7           30      10             {13,17,19,23,29,31,37,41,43,47}
%e A348176 8          165      12                {m +- 2,8,14,16,26,28}
%e A348176 9      8021811      14              {m +- 10,20,22,40,52,58,62}
%e A348176 10  1071065190      16              {m +- 11,23,37,49,53,61,67,79}
%e A348176 11  1613902650      18             {m +- 1,7,23,29,49,77,83,89,97}
%o A348176 (Python)
%o A348176 from sympy import isprime
%o A348176 rec = -1
%o A348176 for n in range(1, 10**10):
%o A348176     d = 1 if n%2 == 0 else 2
%o A348176     ct = 1 if isprime(n) else 0
%o A348176     while n - d > 2:
%o A348176         k = isprime(n+d) + isprime(n-d)
%o A348176         if k == 2: ct += 2
%o A348176         elif k == 1: break
%o A348176         d += 2
%o A348176     if ct > rec: print(n, end = ', '); rec = ct
%Y A348176 Cf. A346399.
%K A348176 nonn,more
%O A348176 1,2
%A A348176 _Ya-Ping Lu_, Oct 05 2021
%E A348176 a(12)-a(13) from _Martin Ehrenstein_, Nov 21 2021