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

Author

Labos Elemer, Jan 03 2002

Keywords

• nonn

Examples

			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.
		

Crossrefs

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

Programs

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}]

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