A321577 - OEIS

%I #20 Dec 06 2021 11:01:44

%S 0,2,5,2,5,17,5,2,257,17,5,17,5,17,257,2,5,1025,5,65537,257,17,5,

%T 65537,129,17,67108865,65537,5,17,5,2,257,17,262145,268435457,5,17,

%U 257,65537,5,4194305,5,65537,131073,17,5,65537,1073741825,16777217,257,65537,5

%N a(n) = F_n mod M_n, where F_n = 2^(2^n) + 1 and M_n = 2^n - 1.

%C Sequence contains all Fermat numbers > 3.

%H Antti Karttunen, <a href="/A321577/b321577.txt">Table of n, a(n) for n = 1..3344</a>

%F For n > 1, a(n) = 2^(2^n mod n) + 1 = A112987(n) + 1.

%t Prepend[1 + 2^Array[PowerMod[2, #, #] &, 85, 2], 0] (* _Michael De Vlieger_, Nov 13 2018, after _Vincenzo Librandi_ at A112987 *)

%o (PARI) apply( A321577(n)=if(n>1,2^lift(Mod(2, n+!n)^n)+1), [0..50]) \\ _M. F. Hasler_, Nov 19 2018

%Y Cf. A000215, A000225, A112987.

%K nonn

%O 1,2

%A _Thomas Ordowski_, Nov 13 2018