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

1,1

Comments

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

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A353740 A090212 A137046 * A156494 A232371 A114878

Adjacent sequences: A104332 A104333 A104334 * A104336 A104337 A104338

Keyword

easy,nonn

Author

Jonathan Vos Post, Apr 17 2005

Extensions

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

Status

approved