A260711 Numbers of the form x^2 - y^2 with x >= y; x and y are odd, x + y is a power of 2.

0, 8, 16, 32, 48, 64, 96, 128, 160, 192, 224, 256, 320, 384, 448, 512, 576, 640, 704, 768, 832, 896, 960, 1024, 1152, 1280, 1408, 1536, 1664, 1792, 1920, 2048, 2176, 2304, 2432, 2560, 2688, 2816, 2944, 3072, 3200, 3328, 3456, 3584, 3712, 3840, 3968, 4096, 4352, 4608, 4864

Offset

1,2

Comments

These binomials do not have primitive factors.

Links

Table of n, a(n) for n=1..51.

Wikipedia, Lucas sequence

Prog

(Magma) lst:=[0]; r:=4864; t:=1; d:=func<t | Floor(r/(4*t))>; while d(t) gt t do s:=d(t); if s mod 2 eq 1 and t mod 2 eq 1 then s-:=1; end if; if s mod 2 eq 0 and t mod 2 eq 0 then s-:=1; end if; repeat; m:=(s+t)^2-(s-t)^2; if PrimeDivisors(s) eq [2] then Append(~lst, m); end if; s-:=2; until s-t lt 1; t+:=1; end while; Sort(lst); // Arkadiusz Wesolowski, Dec 19 2020

Crossrefs

Subsequence of A008590.

Sequence in context: A219547 A259751 A106841 * A139598 A137243 A360124

Adjacent sequences: A260708 A260709 A260710 * A260712 A260713 A260714

Keyword

nonn

Author

Arkadiusz Wesolowski, Jul 30 2015

Status

approved