A104335 Positive integers n such that n^14 + 1 is semiprime (A001358).

4, 74, 94, 116, 270, 464, 556, 654, 1140, 1156, 1246, 1306, 1736, 2464, 2470, 2604, 2804, 2836, 2900, 3054, 3890, 4006, 4056, 4330, 4736, 4780, 5016, 5294, 5340, 5486, 5700, 5834, 6434, 7114, 7304, 8626, 8880, 9164, 9546, 9744, 9980, 10086, 10166

Offset: 1

Author

Jonathan Vos Post, Apr 17 2005

Keywords

• easy
• nonn

Comments

x^14+1 has factors (1 + x^2) (1 - x^2 + x^4 - x^6 + x^8 - x^10 + x^12).

Examples

			4^14 + 1 = 268435457 = 17 * 15790321,
74^14 + 1 = 147653612273582215982104577 = 5477 * 26958848324553992328301,
1140^14 + 1 = 6261349103849104148619671961600000000000001 = 1299601 * 4817901112610027345792802530622860401.
		

Links

• Robert Price, Table of n, a(n) for n = 1..1114

Crossrefs

Cf. A001358, A085722, A096173, A186669, A104238, A103854, A105041, A105066, A105078, A105122, A105142, A105237, A104335, A104479, A104494, A104657, A105282.

Programs

Mathematica

Select[ Range[2, 10422, 2], PrimeQ[ #^2 + 1] && PrimeQ[ #^12 - #^10 + #^8 - #^6 + #^4 - #^2 + 1] &] (*Robert G. Wilson v, Apr 18 2005 *)
Select[Range[2,10200,2],PrimeOmega[#^14+1]==2&] (* Harvey P. Dale, Oct 16 2011 *)

Extensions

More terms from Robert G. Wilson v, Apr 18 2005