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

1,1

Comments

a(0) = 0. - Eduard Roure Perdices, Dec 23 2022

Links

Table of n, a(n) for n=1..13.

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

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.

Cf. A001359, A006988.

Sequence in context: A035341 A258369 A137383 * A047897 A204461 A121144

Adjacent sequences: A049032 A049033 A049034 * A049036 A049037 A049038

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