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A289382 a(n) = 2^n mod triangular(n).

%I A289382 #19 Sep 12 2023 12:19:43
%S A289382 0,1,2,6,2,1,16,4,17,34,2,40,2,4,8,120,104,1,78,46,134,70,140,16,132,
%T A289382 121,134,30,2,94,64,400,206,429,158,334,2,4,8,616,494,1,690,346,692,
%U A289382 142,848,64,912,1024,8,796,797,379,1528,4,350,178,1418,916,2,4,512,1056,32,2011
%N A289382 a(n) = 2^n mod triangular(n).
%H A289382 Seiichi Manyama, <a href="/A289382/b289382.txt">Table of n, a(n) for n = 1..10000</a>
%F A289382 a(n) = A000079(n) mod A000217(n) = 2^n mod n*(n+1)/2.
%F A289382 a(n) = 1 for n>1 in A272934. - _Michel Marcus_, Jul 04 2017
%e A289382 a(6) = 2**6 mod (6*7/2) = 64 mod 21 = 1.
%p A289382 seq(2^n mod n*(n+1)/2, n=1..100); # _Robert Israel_, Jul 04 2017
%t A289382 Table[Mod[2^n, n (n + 1)/2], {n, 66}] (* _Michael De Vlieger_, Jul 04 2017 *)
%t A289382 PowerMod[2,#,(#(#+1))/2]&/@Range[70] (* _Harvey P. Dale_, Oct 12 2018 *)
%o A289382 (Python)
%o A289382 for n in range(1,99): print(str(int(2**n % (n*(n+1)/2))), end=', ')
%o A289382 (PARI) a(n) = lift(Mod(2, n*(n+1)/2)^n); \\ _Michel Marcus_, Jul 04 2017
%Y A289382 Cf. A000079, A000217, A066606, A272934.
%K A289382 nonn
%O A289382 1,3
%A A289382 _Alex Ratushnyak_, Jul 04 2017