A179921 a(n) = prime(n) if n<=3; for n>3, a(n) is the smallest prime >a(n-1), such that the denominator of fraction (a(n-1)-a(n-2))/(a(n)-a(n-1)) did not appear earlier.

2, 3, 5, 7, 13, 23, 31, 53, 67, 79, 113, 131, 151, 193, 233, 271, 307, 353, 379, 409, 457, 557, 613, 691, 761, 809, 883, 907, 1013, 1069, 1123, 1181, 1213, 1279, 1361, 1423, 1483, 1571, 1657, 1709, 1811, 1933, 1997, 2087, 2179, 2273, 2341, 2459

Offset

1,1

Comments

Using Dirichlet's theorem on arithmetic progressions, it is easy to prove that the sequence is infinite. The sequence of the corresponding denominators begins with 2,1,3,5,4,11,7,6,17, ...

Links

Table of n, a(n) for n=1..48.

Example

The first four terms 2,3,5,13 give three denominators: 2,1,3. Then a(5) is not in {17, 19}, since (13-5)/(17-13) = 2/1, (13-5)/(19-13) = 4/3 and denominators 1 and 3 already appeared earlier. Since (13-5)/(23-13) = 4/5 and 5 is not yet in the denominator sequence, a(5) = 23.

Crossrefs

Cf. A168253, A178942, A179210, A179234, A179256, A179328.

Sequence in context: A163487 A048413 A064336 * A211073 A182315 A233862

Adjacent sequences: A179918 A179919 A179920 * A179922 A179923 A179924

Keyword

nonn

Author

Vladimir Shevelev, Jan 12 2011

Extensions

Edited by Alois P. Heinz, Jan 12 2011

Status

approved