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 A212274 Minimal k >= 5n such that n^2 + 2nk + k is a perfect square. 0
 5, 12, 16, 20, 64, 76, 49, 100, 112, 64, 136, 148, 160, 172, 184, 105, 120, 220, 120, 244, 256, 121, 280, 292, 161, 316, 144, 176, 352, 364, 221, 217, 400, 217, 424, 436, 232, 225, 472, 484, 496, 288, 273, 532, 225, 288, 253, 580, 352, 604, 616, 276, 640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Without any restriction, trivially, a(n)=0 and, if to consider a(n) positive, then, again trivially, a(n)=1. Without the restriction k >= 5n, we have a(n)=4*n+1; on the other hand, if to require a(n)>=5*n and in addition a(n+1)>a(n), then we obtain sequence 5,12,16,20 and, beginning with n=5, we have progression 64+12*(n-5). LINKS MATHEMATICA Table[k = 5*n; While[! IntegerQ[Sqrt[n^2 + 2*n*k + k]], k++]; k, {n, 100}] (* T. D. Noe, May 18 2012 *) CROSSREFS Sequence in context: A178469 A314277 A314278 * A301714 A314279 A314280 Adjacent sequences:  A212271 A212272 A212273 * A212275 A212276 A212277 KEYWORD nonn AUTHOR Vladimir Shevelev and Peter J. C. Moses, May 13 2012 STATUS approved

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Last modified May 15 15:52 EDT 2021. Contains 343920 sequences. (Running on oeis4.)