A078515
Numbers n such that A053597(n) sets a new record.
Original entry on oeis.org
1, 7, 23, 30, 94, 219, 279, 773, 1856, 3724, 6999, 7000, 19205, 184163, 280103, 849876, 1870722, 3570761, 4114341, 11271072, 55282774, 68256040, 68256041, 104011359, 1009322491, 1311699253, 7889803997
Offset: 1
-
f[n_] := Block[{k = 1}, While[p = Table[ Prime[i], {i, n, n + k}]; Length[ Union[Drop[p, 1] - Drop[p, -1]]] == k, k++ ]; k - 1]; a = Table[0, {50}]; Do[b = f[n]; If[ a[[b]] == 0, a[[b]] = n], {n, 1, 19000000}]
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.
Original entry on oeis.org
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
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.
-
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}]
Showing 1-2 of 2 results.