A186312 - OEIS

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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

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OFFSET

1,1

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)).

Sequence in context: A168539 A320882 A048524 * A142401 A139859 A217114

Adjacent sequences: A186309 A186310 A186311 * A186313 A186314 A186315

KEYWORD

nonn

AUTHOR

T. D. Noe, Feb 17 2011

STATUS

approved