A274595 Numbers n such that n^2 + 2 is the sum of two nonzero squares.

0, 4, 12, 24, 40, 48, 60, 68, 72, 84, 104, 112, 132, 140, 144, 148, 176, 180, 192, 204, 216, 220, 252, 264, 276, 284, 312, 320, 324, 364, 372, 384, 392, 396, 408, 420, 428, 444, 456, 468, 472, 480, 528, 544, 588, 600, 612, 624, 636, 644, 648, 660, 684, 688, 708, 720

Offset

1,2

Comments

All terms are divisible by 4.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

12 is a term because 12^2 + 2 = 5^2 + 11^2.

Maple

f:= n -> andmap(t -> t[1] mod 4 <> 3 or t[2]::even, ifactors(n^2+2)[2]):
map(f, [seq(n, n=4..1000, 4)]); # Robert Israel, Jul 12 2016

Mathematica

stnsQ[n_]:=Length[Select[IntegerPartitions[n^2+2, {2}], AllTrue[Sqrt[ #], IntegerQ]&]]>0; Select[Range[0, 750, 4], stnsQ]  (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 11 2020 *)

Prog

(PARI) isA000404(n) = for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2));
lista(nn) = for(n=0, nn, if(isA000404(n^2+2), print1(n, ", ")));

Crossrefs

Cf. A000404, A059100.

Sequence in context: A301058 A008213 A008187 * A115228 A081935 A008006

Adjacent sequences: A274592 A274593 A274594 * A274596 A274597 A274598

Keyword

nonn,easy

Author

Altug Alkan, Jun 30 2016

Status

approved