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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
 84, 36, 7, 7, 27, 18821, 18, 9, 18, 77, 9, 66, 66, 9, 15488, 55, 55, 62025, 9, 44, 9, 1547, 33, 11, 336, 96, 11, 11, 2667, 1462, 182, 11, 22, 246, 22, 11, 22, 143, 143, 11, 11, 11, 11, 48, 117, 3762, 11, 495, 117, 130, 11, 104, 832, 435, 11, 13, 91, 91, 405, 5445 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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]). LINKS EXAMPLE 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. MATHEMATICA a = {}; Do[k = 1; While[ !IntegerQ[ Sqrt[k^2 + (Prime[n + k] - Prime[n])^2]], k++ ]; a = Append[a, k], {n, 1, 60} ]; a CROSSREFS Sequence in context: A317437 A304379 A317916 * A008898 A033404 A252723 Adjacent sequences:  A066686 A066687 A066688 * A066690 A066691 A066692 KEYWORD nonn AUTHOR Joseph L. Pe, Jan 11 2002 EXTENSIONS More terms from Robert G. Wilson v, Jan 13 2002 STATUS approved

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Last modified September 26 13:21 EDT 2021. Contains 347668 sequences. (Running on oeis4.)