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 A066689 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. 0

%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

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Last modified October 19 16:25 EDT 2021. Contains 348091 sequences. (Running on oeis4.)