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%I #11 Oct 19 2017 03:14:09
%S 2,2,2,17,83,113,491,1367,1801,5869,15919,34883,70639,70657,214867,
%T 214867,2515871,3952733,13010143,30220163,60155567,69931991,203674907,
%U 1092101119,1363592621,1363592677,2124140323,23024158649,30282104173,30282104173,196948778371
%N a(n) = smallest prime p_k such that the n successive differences between the primes p_k through p_(k+n) are all distinct.
%e 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.
%e 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.
%t 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}]
%Y Cf. A001223, A068843, A053597, A078515. Different from A079889.
%K nonn
%O 0,1
%A _Labos Elemer_, Jan 03 2002
%E Edited by _Robert G. Wilson v_ and _N. J. A. Sloane_, Jan 05 2002
%E More terms from _Don Reble_, Jan 15 2003
%E a(27)-a(30) from _Donovan Johnson_, Oct 23 2012
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