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%I #43 Oct 05 2022 17:19:27
%S 1,5,13,29,37,61,73,157,181,193,277,313,397,421,457,541,561,613,661,
%T 673,733,757,877,997,1093,1153,1201,1213,1237,1289,1321,1381,1453,
%U 1621,1657,1753,1873,1905,1933,1993,2017,2137,2341,2473,2557,2593,2797,2857,2917
%N Numbers n such that 2^n == 2 (mod n*(n+1)).
%C a(17) = 561 is the first composite number in the sequence. - _Charles R Greathouse IV_, Sep 19 2012
%C Intersection of { A015919(n) } and { A192109(n)-1 }. - _Max Alekseyev_, Apr 22 2013
%H V. Raman and Charles R Greathouse IV, <a href="/A216822/b216822.txt">Table of n, a(n) for n = 1..10000</a> (first 2000 terms from V. Raman)
%H Mersenne Forum, <a href="http://mersenneforum.org/showthread.php?t=17198">Prime Conjecture</a>
%t Select[Range[1, 10000], Mod[2^# - 2, # (# + 1)] == 0 &] (* _T. D. Noe_, Sep 19 2012 *)
%t Join[{1},Select[Range[3000],PowerMod[2,#,#(#+1)]==2&]] (* _Harvey P. Dale_, Oct 05 2022 *)
%o (PARI) is(n)=Mod(2,n*(n+1))^n==2; \\ _Charles R Greathouse IV_, Sep 19 2012
%o (Python)
%o A216822_list = [n for n in range(1,10**6) if n == 1 or pow(2,n,n*(n+1)) == 2] # _Chai Wah Wu_, Mar 25 2021
%Y Cf. A069051 (prime n such that 2^n == 2 (mod n*(n-1))).
%Y Cf. A217466 (prime terms of the sequence).
%Y Cf. A217465 (composite terms of the sequence)
%K easy,nonn
%O 1,2
%A _V. Raman_, Sep 17 2012
%E a(1)=1 prepended by _Max Alekseyev_, Dec 29 2017
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