A079007 a(n) = smallest prime p_k such that the n successive differences between the primes p_k through p_(k+n) are all distinct.

2, 2, 2, 17, 83, 113, 491, 1367, 1801, 5869, 15919, 34883, 70639, 70657, 214867, 214867, 2515871, 3952733, 13010143, 30220163, 60155567, 69931991, 203674907, 1092101119, 1363592621, 1363592677, 2124140323, 23024158649, 30282104173, 30282104173, 196948778371

Offset

0,1

Links

Table of n, a(n) for n=0..30.

Example

a(0) = 2; a(1) = 2 from {2,3} with a single difference 1; a(2) = 2 from {2,3,5}, with two distinct differences 1, 2.
a(5) = p_30 = 113 because 113 is followed by 127, 131, 137, 139, 149, with 5 different differences: 14, 4, 6, 2, 10; and no smaller prime has this property.

Mathematica

f[k_, n_] := Block[{p = Table[ Prime[i], {i, k, k + n - 1}]}, Length[ Union[Drop[p, 1] - Drop[p, -1]]]]; k = 1; Do[ While[ f[k, n] != n - 1, k++ ]; Print[ Prime[k]], {n, 1, 22}]

Crossrefs

Cf. A001223, A068843, A053597, A078515. Different from A079889.

Sequence in context: A346079 A195871 A214756 * A349642 A064215 A358633

Adjacent sequences: A079004 A079005 A079006 * A079008 A079009 A079010

Keyword

nonn

Author

Labos Elemer, Jan 03 2002

Extensions

Edited by Robert G. Wilson v and N. J. A. Sloane, Jan 05 2002

More terms from Don Reble, Jan 15 2003

a(27)-a(30) from Donovan Johnson, Oct 23 2012

Status

approved