A213353 A subset of numbers n such that n^4 is a Sierpinski number.

44745755, 1812338107, 9266824499, 12308871853, 13657352875, 22767480811, 22930161667, 24068927659, 25549554505, 25770503549, 57939582163, 90219135299, 90329609821, 96949951147, 103126759951

Offset: 1

Author

Arkadiusz Wesolowski, Jun 09 2012

Keywords

• nonn
• easy
• fini
• full

Comments

A sequence constructed from Izotov's trick.

If n belongs to this sequence and n does not end in 5, then n^4 has the covering set {3, 5, 17, 97, 241, 257, 673}.

Links

• Anatoly S. Izotov, A note on Sierpinski numbers
• Wikipedia, Sierpinski number

Crossrefs

Subset of A233469. Cf. A076336.

Programs

Mathematica

(* even if nn is increased, no additional terms are generated *) nn = 14; lst = {}; n = 44745755; p = 2^12; m = 3*(p^4 - 1)/(p - 1); Do[a = n + (-1)^c*m; n = a/GCD[a, p]; AppendTo[lst, Abs@n], {c, 0, nn}]; Union@lst