A049035 Number of pairs of twin primes whose smaller element is <= 10^n-th prime.
5, 25, 174, 1270, 10250, 86027, 738597, 6497407, 58047180, 524733511, 4789919653, 44073509102, 408231310520
Offset: 1
Examples
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}.
Links
- Soren Laing Aletheia-Zomlefer, Lenny Fukshansky, and Stephan Ramon Garcia, The Bateman-Horn Conjecture: Heuristics, History, and Applications, arXiv:1807.08899 [math.NT], 2018-2019. See Table 5 p. 40.
- Index entries for sequences related to numbers of primes in various ranges
Programs
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Python
from sympy import prime, sieve # use primerange for larger terms def afind(terms): c, prevp = 0, 1 for n in range(1, terms+1): for p in sieve.primerange(prevp+1, prime(10**n)+3): if prevp == p - 2: c += 1 prevp = p print(c, end=", ") afind(6) # Michael S. Branicky, Apr 25 2021
Extensions
More terms from Labos Elemer, Oct 13 2000; Jud McCranie, Dec 30 2000
a(9) from Michael S. Branicky, Apr 25 2021
a(10) from Eduard Roure Perdices, May 08 2021
a(11) from Eduard Roure Perdices, Feb 03 2022
a(12) from Eduard Roure Perdices, Dec 23 2022
a(13) from Eduard Roure Perdices, Jan 24 2024
Comments