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

2, 4, 5, 7, 8, 10, 11, 14, 16, 19, 20, 22, 23, 26, 29, 31, 34, 35, 37, 40, 41, 44, 49, 50, 52, 53, 55, 56, 64, 65, 68, 70, 74, 76, 79, 82, 83, 86, 89, 91, 95, 97, 98, 100, 106, 112, 113, 115, 116, 119

Offset: 1

Author

Wolfdieter Lang, Mar 14 2012

Keywords

• nonn

Comments

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.

Examples

			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, ...
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.
		

Links

• Jon Maiga, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001748, A208296.

Programs

Mathematica

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 *)

Formula

a(n) = (3*prime(n+2) - A208296(n))/2, with the primes prime(n+2) = A000040(n+2), n>=1.