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

1,1

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.

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A001748, A208296.

Sequence in context: A229973 A007951 A237590 * A213539 A190849 A277121

Adjacent sequences: A207333 A207334 A207335 * A207337 A207338 A207339

Keyword

nonn

Author

Wolfdieter Lang, Mar 14 2012

Status

approved