A212274 Minimal k >= 5n such that n^2 + 2nk + k is a perfect square.

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

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

Table of n, a(n) for n=1..53.

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