A186312 There appear to be at least n lower twin primes between x/2 and x for all x >= a(n).

11, 59, 101, 149, 179, 227, 569, 599, 641, 809, 821, 1019, 1049, 1061, 1289, 1319, 1427, 1451, 1481, 1667, 1787, 1871, 1877, 1931, 1949, 2081, 2129, 2237, 2657, 2687, 2711, 2999, 3251, 3257, 3299, 3359, 3461, 3467, 3527, 3539, 3767, 3917, 4001, 4019, 4091

Offset: 1

Author

T. D. Noe, Feb 17 2011

Keywords

• nonn

Comments

The name says "appear" because this sequence assumes that the twin prime conjecture is true. Note that every term is also a lower twin prime. This sequence for lower twin primes is like the Ramanujan primes (A104272) for the sequence of prime numbers. However, in this case, we do not know if there are an infinite number of twin primes. It appears that A001359(2n) < a(n) < A001359(4n).

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001359 (lower twin primes), A088018 (counts the lower twin primes between n-1 and 2(n-1)).