A104494 Positive integers n such that n^17 + 1 is semiprime (A001358).

2, 58, 66, 166, 268, 270, 408, 600, 672, 808, 822, 970, 1050, 1090, 1150, 1200, 1212, 1380, 1578, 1752, 1912, 1950, 1986, 2016, 2038, 2292, 2340, 2548, 2590, 2656, 2718, 2800, 2856, 3162, 3300, 3342, 3738, 4138, 4152, 4228, 4270, 4272, 4362, 4782, 5080, 5166

Offset

1,1

Links

Robert Price, Table of n, a(n) for n = 1..1000

Formula

a(n)^17 + 1 is semiprime (A001358).

Example

2^17 + 1 = 131073 = 3 * 43691,
58^17 + 1 = 951208868148684143308060622849 = 59 * 16122184205909900734034925811,
66^17 + 1 = 8555529718761317069203003539457 = 67 * 127694473414348015958253784171,
1050^17 + 1 = 2292018317801032401637344360351562500000000000000001 = 1051 * 2180797638250268698037435166842590390104662226451.

Mathematica

Select[Range[1000000], PrimeQ[# + 1] && PrimeQ[(#^17 + 1)/(# + 1)] &] (* Robert Price, Mar 10 2015 *)
Select[Range[5200], PrimeOmega[#^17+1]==2&] (* Harvey P. Dale, Mar 07 2017 *)

Prog

(PARI) for(n=1, 3000, if(!ispseudoprime(n^17+1), forprime(p=1, 10^4, if((n^17+1)%p==0, if(ispseudoprime((n^17+1)/p), print1(n, ", ")); break)))) \\ Derek Orr, Mar 09 2015
(Magma) IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [n: n in [1..1200]|IsSemiprime(n^17+1)]; // Vincenzo Librandi, Mar 10 2015

Crossrefs

Cf. A001358, A006313, A103854, A104238, A104335, A105041, A105066, A105078, A105122, A105142, A105237, A104479.

Sequence in context: A030263 A359242 A090743 * A121931 A343578 A156507

Adjacent sequences: A104491 A104492 A104493 * A104495 A104496 A104497

Keyword

easy,nonn

Author

Jonathan Vos Post, Apr 19 2005

Extensions

a(14)-a(46) from Robert Price, Mar 09 2015

Status

approved