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A207336 One half of smallest positive nontrivial even solution of the congruence x^2 == 1 (mod A001748(n+2)), n>=1.

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%I A207336 #14 Sep 28 2019 12:40:29
%S A207336 2,4,5,7,8,10,11,14,16,19,20,22,23,26,29,31,34,35,37,40,41,44,49,50,
%T A207336 52,53,55,56,64,65,68,70,74,76,79,82,83,86,89,91,95,97,98,100,106,112,
%U A207336 113,115,116,119
%N A207336 One half of smallest positive nontrivial even solution of the congruence x^2 == 1 (mod A001748(n+2)), n>=1.
%C A207336 See the comments on A208296, which gives the representatives of the odd nontrivial solutions of the congruence x^2 == 1 (mod 3*prime(n+2)), with primes prime(n+2)=A000040(n+2), n>=1.
%H A207336 Jon Maiga, <a href="/A207336/b207336.txt">Table of n, a(n) for n = 1..1000</a>
%F A207336 a(n) = (3*prime(n+2) - A208296(n))/2, with the primes prime(n+2) = A000040(n+2), n>=1.
%e A207336 The actual solutions are 4, 8, 10, 14, 16, 20, 22, 28, 32, 38, 40, 44, 46, 52, 58, 62, 68, 70, 74, 80, 82, 88, 98, 100, 104, 106, 110, 112, 128, 130, 136, 140, 148, 152, 158, 164, 166, 172, 178, 182, 190, 194, 196, 200, 212, 224, 226, 230, ...
%e A207336 n=4: 2*a(4) = 14 = 3*13 - 25. 14^2 = 196 == 1 (mod 39), 25^2 = 625 == 1 (mod 39). Representatives of the trivial solutions are 1 and 39-1= 38. All-together there are 4 incongruent solutions.
%t A207336 Table[(3*Prime[n+2]-SelectFirst[Solve[x^2==1 && x !=1,x,Modulus->3*Prime[n+2]][[All,1,2]],OddQ])/2, {n, 50}] (* _Jon Maiga_, Sep 28 2019 *)
%Y A207336 Cf. A001748, A208296.
%K A207336 nonn
%O A207336 1,1
%A A207336 _Wolfdieter Lang_, Mar 14 2012