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A049035 Number of pairs of twin primes whose smaller element is <= 10^n-th prime. 1
5, 25, 174, 1270, 10250, 86027, 738597, 6497407, 58047180, 524733511, 4789919653, 44073509102, 408231310520 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(0) = 0. - Eduard Roure Perdices, Dec 23 2022
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.
EXAMPLE
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}.
PROG
(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
CROSSREFS
See A093683 for another version.
Sequence in context: A035341 A258369 A137383 * A047897 A204461 A121144
KEYWORD
nonn,more
AUTHOR
Dennis S. Kluk (mathemagician(AT)ameritech.net)
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
STATUS
approved

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Last modified July 24 07:52 EDT 2024. Contains 374575 sequences. (Running on oeis4.)