A099154 Largest number k such that the interval [k^2,(k+1)^2] contains not more than n pairs of twin primes.

122, 213, 502, 545, 922, 950, 749, 1098, 1330, 1450, 1634, 1623, 2135, 2110, 2177, 2244, 2760, 2413, 2556, 3280, 3454, 3211, 3740, 3540, 4104, 4096, 4391, 4457, 4592, 5309, 4758, 5720, 5747, 5295, 5902, 5456, 5920, 6395, 5810, 7007, 7109, 7450, 7540

Offset

0,1

Comments

The terms of this sequence are conjectural, even under the twin prime conjecture.

Links

Table of n, a(n) for n=0..42.

Eric Weisstein's World of Mathematics, Twin Primes.

Eric Weisstein's World of Mathematics, Twin Prime Conjecture.

Example

a(1)=213 because the interval [213^2,214^2]=[45369,45796] contains one pair of twin primes (45587,45589) whereas all higher intervals are conjectured to contain at least two pairs of twin primes.
The interval [122^2,123^2]=[A091592(11)^2,(A091592(11)+1)^2] is conjectured to be the last interval between two consecutive squares containing no twin primes.

Crossrefs

Cf. A091591 number of pairs of twin primes between n^2 and (n+1)^2, A091592 numbers n such that there are no twin primes between n^2 and (n+1)^2, A014574.

Sequence in context: A222578 A105983 A356369 * A304605 A158131 A004925

Adjacent sequences: A099151 A099152 A099153 * A099155 A099156 A099157

Keyword

nonn

Author

Hugo Pfoertner, Sep 30 2004

Status

approved