1,1

We have the polynomial factorization: n^22 + 1 = (n^2 + 1) * (n^20 - n^18 + n^16 - n^14 + n^12 - n^10 + n^8 - n^6 + n^4 - n^2 + 1). Hence after the initial n=1 prime, the binomial can never be prime. It can be semiprime iff n^2+1 is prime and (n^20 - n^18 + n^16 - n^14 + n^12 - n^10 + n^8 - n^6 + n^4 - n^2 + 1) is prime.

a(n)^22 + 1 is in A001358. a(n)^2+1 is in A000040 and (a(n)^20 - a(n)^18 + a(n)^16 - a(n)^14 + a(n)^12 - a(n)^10 + a(n)^8 - a(n)^6 + a(n)^4 - a(n)^2 + 1) is in A000040.

116^22 + 1 = 2618639792014920380336685706161496723088736257 = 13457 * 194593133091693570657404005808240820620401,

300^22 + 1 = 3138105960900000000000000000000000000000000000000000001 = 90001 * 34867456593815624270841435095165609271008099910001,

950^22 + 1 = 323533544973709366507562922501564025878906250000000000000000000001 = 902501 * 358485525194663902319845543109164450653136395416736380347501.

Cf. A000040, A001358, A006313, A103854, A104238, A104335, A105041, A105066, A105078, A105122, A105142, A105237, A104479, A104494, A104657, A105282.

Sequence in context: A056101 A051116 A095623 this_sequence A096925 A097231 A076044

Adjacent sequences: A105931 A105932 A105933 this_sequence A105935 A105936 A105937

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Apr 26 2005