

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.


9



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
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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: A161748 A195871 A214756 * A064215 A087238 A226935
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



