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Composite values of n such that 2^n == 2 (mod n*(n-1)).
7

%I #27 Dec 29 2017 20:27:28

%S 91625794219,8796093022207,1557609722332488343,18216643597893471403

%N Composite values of n such that 2^n == 2 (mod n*(n-1)).

%C No other terms below 2^64.

%C The next term is <= 25790417485109157029391019 = A019320(258). - _Emmanuel Vantieghem_, Dec 01 2014

%C Terms A019320(k) belongs to this sequence for k in A297412. - _Max Alekseyev_, Dec 29 2017

%H Mersenne Forum, <a href="http://mersenneforum.org/showthread.php?t=17198">Prime Conjecture</a>

%e a(1) = 91625794219 = (2^38 - 2^19 + 1)/3 = A019320(114).

%e a(2) = 8796093022207 = 2^43 - 1 = A019320(43).

%o (PARI) is_A217468(n)={Mod(2,(n-1)*n)^n==2 & !isprime(n)} \\ - _M. F. Hasler_, Oct 07 2012

%Y Cf. A069051, A216822, A219037, A217465.

%Y Intersection of A001567 and { 2*A014945(k) + 1 }.

%K nonn,hard,more

%O 1,1

%A _V. Raman_, Oct 04 2012