A061369 a(n) = smallest square in the arithmetic progression {nk+1 : k > 0}.

4, 9, 4, 9, 16, 25, 36, 9, 64, 81, 100, 25, 144, 169, 16, 49, 256, 289, 324, 81, 64, 441, 484, 25, 576, 625, 676, 169, 784, 121, 900, 225, 100, 1089, 36, 289, 1296, 1369, 196, 81, 1600, 169, 1764, 441, 361, 2025, 2116, 49, 2304, 2401, 256, 625, 2704, 2809, 441

Offset

1,1

Links

Table of n, a(n) for n=1..55.

Formula

a(n)=Min{x^2 : x^2=nk+1}

Example

Each square q appears in several progressions, i.e. in A000005(q-1) cases. Not necessarily as a first square. E.g. q=81 is minimal in {10k+1},{20k+1},{40k+1},{80k+1}, while not minimal in {3k+1} and 5 other progressions. In {16k+1} 49 comes before 81.

Crossrefs

Sequence in context: A061767 A131016 A204996 * A361400 A291645 A340769

Adjacent sequences: A061366 A061367 A061368 * A061370 A061371 A061372

Keyword

nonn

Author

Labos Elemer, Jun 08 2001

Status

approved