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%I #17 Jul 01 2021 23:43:40
%S 1,1,1,2,1,2,2,2,2,1,2,2,2,2,2,3,3,2,2,2,3,3,4,4,3,3,4,4,5,4,4,4,4,4,
%T 4,4,4,4,4,3,3,4,4,4,3,3,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,
%U 4,3,3,2,3,3,3,3,3,3,3,4,4,4,4,5,5,5,5
%N Number of twin prime pairs in the range (6*n + 1, 6*(n + m) + 1], where m is the number of twin prime pairs, 6*k +- 1 for k = 1, 2, ..., n.
%C Conjecture: a(n) >= 1.
%o (Python)
%o from sympy import isprime
%o def istwin(m): return 1 if isprime(6*m-1)*isprime(6*m+1) == 1 else 0
%o ct1 = 0
%o for n in range(1, 100):
%o ct1 += istwin(n); ct = 0
%o for m in range (n + 1, n + ct1 + 1): ct += istwin(m)
%o print(ct)
%Y Cf. A071538, A079629, A080356, A237840, A332086, A337788.
%K nonn
%O 1,4
%A _Ya-Ping Lu_, Jun 24 2021
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