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A049035 Number of pairs of twin primes whose smaller element is <= 10^n-th prime.

%I A049035 #42 Jan 24 2024 08:01:01
%S A049035 5,25,174,1270,10250,86027,738597,6497407,58047180,524733511,
%T A049035 4789919653,44073509102,408231310520
%N A049035 Number of pairs of twin primes whose smaller element is <= 10^n-th prime.
%C A049035 a(0) = 0. - _Eduard Roure Perdices_, Dec 23 2022
%H A049035 Soren Laing Aletheia-Zomlefer, Lenny Fukshansky, and Stephan Ramon Garcia, <a href="https://arxiv.org/abs/1807.08899">The Bateman-Horn Conjecture: Heuristics, History, and Applications</a>, arXiv:1807.08899 [math.NT], 2018-2019. See Table 5 p. 40.
%H A049035 <a href="/index/Pri#primepop">Index entries for sequences related to numbers of primes in various ranges</a>
%e A049035 a(1) = 5 since the 10th prime is 29 and the first 5 twin primes are {3,5}, {5,7}, {11,13}, {17,19} and {29,31}.
%o A049035 (Python)
%o A049035 from sympy import prime, sieve # use primerange for larger terms
%o A049035 def afind(terms):
%o A049035   c, prevp = 0, 1
%o A049035   for n in range(1, terms+1):
%o A049035     for p in sieve.primerange(prevp+1, prime(10**n)+3):
%o A049035       if prevp == p - 2: c += 1
%o A049035       prevp = p
%o A049035     print(c, end=", ")
%o A049035 afind(6) # _Michael S. Branicky_, Apr 25 2021
%Y A049035 See A093683 for another version.
%Y A049035 Cf. A001359, A006988.
%K A049035 nonn,more
%O A049035 1,1
%A A049035 Dennis S. Kluk (mathemagician(AT)ameritech.net)
%E A049035 More terms from _Labos Elemer_, Oct 13 2000; _Jud McCranie_, Dec 30 2000
%E A049035 a(9) from _Michael S. Branicky_, Apr 25 2021
%E A049035 a(10) from _Eduard Roure Perdices_, May 08 2021
%E A049035 a(11) from _Eduard Roure Perdices_, Feb 03 2022
%E A049035 a(12) from _Eduard Roure Perdices_, Dec 23 2022
%E A049035 a(13) from _Eduard Roure Perdices_, Jan 24 2024