%I
%S 84,36,7,7,27,18821,18,9,18,77,9,66,66,9,15488,55,55,62025,9,44,9,
%T 1547,33,11,336,96,11,11,2667,1462,182,11,22,246,22,11,22,143,143,11,
%U 11,11,11,48,117,3762,11,495,117,130,11,104,832,435,11,13,91,91,405,5445
%N Least number k such that the square root of {k^2 + (Prime[n + k]  Prime[n])^2} is an integer; or 0 if no such number exists.
%C The square root of {k^2 + (Prime[n + k]  Prime[n])^2} = distance between the points (n,Prime[n]) and (n+k,Prime[n+k]).
%e k = 84 is the least k such that d[(1,p(1)),(1+k,p(1+k))] = Sqrt[k^2 + (p(1 + k)  p(1))^2] (= 445) is an integer; so a(1) = 84.
%t a = {}; Do[k = 1; While[ !IntegerQ[ Sqrt[k^2 + (Prime[n + k]  Prime[n])^2]], k++ ]; a = Append[a, k], {n, 1, 60} ]; a
%K nonn
%O 1,1
%A _Joseph L. Pe_, Jan 11 2002
%E More terms from _Robert G. Wilson v_, Jan 13 2002
