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A113396 a(n) = -prime(n)^2 (mod prime(n+1)).

%I A113396 #21 Feb 02 2025 14:16:42
%S A113396 2,1,3,6,9,1,15,7,22,27,1,25,39,31,17,23,57,31,55,69,43,67,53,33,85,
%T A113396 99,91,105,97,58,115,101,135,49,147,121,127,151,137,143,177,91,189,
%U A113396 181,195,67,79,211,225,217,203,237,151
%N A113396 a(n) = -prime(n)^2 (mod prime(n+1)).
%H A113396 Harvey P. Dale, <a href="/A113396/b113396.txt">Table of n, a(n) for n = 1..1000</a>
%F A113396 a(n) = prime(n+1) - A167770(n). - _Jason Yuen_, Sep 08 2024
%e A113396 -2^2 == 2 (mod 3); -3^2 == 1 (mod 5); -5^2 == 3 (mod 7); -7^2 == 6 (mod 11); etc.
%t A113396 Mod[#[[2]]^2-#[[1]]^2,#[[2]]]&/@Partition[Prime[Range[60]],2,1] (* _Harvey P. Dale_, Nov 10 2014 *)
%o A113396 (PARI) vector(55,n,(-prime(n)^2)%prime(n+1)) \\ _Joerg Arndt_, Sep 09 2024
%Y A113396 Cf. A000040, A069482, A167770.
%K A113396 nonn,easy
%O A113396 1,1
%A A113396 _Marian Kraus_, Oct 26 2005
%E A113396 Name simplified by _Joerg Arndt_, Sep 09 2024