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

Author

Arkadiusz Wesolowski, Jul 30 2015

Keywords

• nonn

Comments

These binomials do not have primitive factors.

Links

• Wikipedia, Lucas sequence

Crossrefs

Subsequence of A008590.

Programs

Magma

lst:=[0]; r:=4864; t:=1; d:=func; 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