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A217465 Composite integers k such that 2^k == 2 (mod k*(k+1)).

%I A217465 #31 Aug 29 2024 08:51:41
%S A217465 561,1905,4033,4681,5461,6601,8481,11305,13741,13981,16705,23377,
%T A217465 30121,31417,41041,49141,52633,57421,88357,88561,101101,107185,121465,
%U A217465 130561,162193,196021,196093,204001,208465,219781,266305,276013,278545,282133,285541,314821,334153,341497,390937,399001
%N A217465 Composite integers k such that 2^k == 2 (mod k*(k+1)).
%C A217465 Terms A019320(k) belongs to this sequence for k in A297415. - _Max Alekseyev_, Dec 29 2017
%H A217465 Amiram Eldar, <a href="/A217465/b217465.txt">Table of n, a(n) for n = 1..12766</a> (terms below 10^12; terms 1..100 from Harvey P. Dale)
%H A217465 Mersenne Forum, <a href="http://mersenneforum.org/showthread.php?t=17198">Prime Conjecture</a>, 2012.
%t A217465 Select[Range[400000],!PrimeQ[#]&&PowerMod[2,#,#(#+1)]==2&] (* _Harvey P. Dale_, Oct 12 2012 *)
%o A217465 (PARI) for(n=1,10000,if((2^n)%(n*(n+1))==2&&isprime(n)==0,printf(n",")))
%o A217465 (PARI) forcomposite(n=4,10^6, if(Mod(2,n*(n+1))^n==2, print1(n", "))) \\ _Charles R Greathouse IV_, Aug 29 2024
%o A217465 (Python)
%o A217465 from sympy import isprime
%o A217465 A217465_list = [n for n in range(1,10**6) if pow(2,n,n*(n+1)) == 2 and not isprime(n)] # _Chai Wah Wu_, Mar 25 2021
%Y A217465 Subsequence of A216822.
%Y A217465 Contains A303531 as a subsequence.
%Y A217465 Cf. A019320, A217466, A217468, A297415, A298758.
%K A217465 nonn
%O A217465 1,1
%A A217465 _V. Raman_, Oct 04 2012