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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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 26 03:19 EDT 2021. Contains 347664 sequences. (Running on oeis4.)